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Volumn 1971, Issue , 2009, Pages 1-200

Hydrodynamic limits of the boltzmann equation

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EID: 65349138242     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (147)

References (113)
  • 1
    • 0347567539 scopus 로고
    • Spaces of functions with differential difference characteristics and smoothness of the solutions of the transport equations
    • V.I. Agoshkov: Spaces of functions with differential difference characteristics and smoothness of the solutions of the transport equations, Dokl. Akad. Nauk SSSR 276 (1984), 1289-1293.
    • (1984) Dokl. Akad. Nauk SSSR , vol.276 , pp. 1289-1293
    • Agoshkov, V.I.1
  • 2
    • 85009365065 scopus 로고    scopus 로고
    • J.-P. Aubin: Un théorème de compacité., C. R. Acad. Sci. Paris 256 (1963), 5042-5044.
    • J.-P. Aubin: Un théorème de compacité., C. R. Acad. Sci. Paris 256 (1963), 5042-5044.
  • 3
    • 0000469206 scopus 로고
    • Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport
    • C Bardos: Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport, Ann. Scient. Ec. Norm. Sup. 3 (1970), 185-233.
    • (1970) Ann. Scient. Ec. Norm. Sup , vol.3 , pp. 185-233
    • Bardos, C.1
  • 4
    • 0001076950 scopus 로고
    • Fluid Dynamic Limits of the Boltzmann Equation I
    • C. Bardos, F. Golse, CD. Levermore: Fluid Dynamic Limits of the Boltzmann Equation I, J. Stat, Phys. 63 (1991), 323-344.
    • (1991) J. Stat, Phys , vol.63 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 5
    • 84990619144 scopus 로고
    • Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation
    • C. Bardos, F. Golse, CD. Levermore: Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation, Comm. Pure & Appl. Math 46 (1993), 667-753.
    • (1993) Comm. Pure & Appl. Math , vol.46 , pp. 667-753
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 7
    • 0001315807 scopus 로고
    • The classical incompressible Navier-Stokes limit of the Boltzmann equation
    • G. Bardos, S. Ukai: The classical incompressible Navier-Stokes limit of the Boltzmann equation, Math. Models and Methods in the Appl. Sci. 1 (1991), 235-257.
    • (1991) Math. Models and Methods in the Appl. Sci , vol.1 , pp. 235-257
    • Bardos, G.1    Ukai, S.2
  • 8
    • 0038391351 scopus 로고    scopus 로고
    • A formalism for the differentiation of conservation laws
    • C. Bardos, O. Pironneau. A formalism for the differentiation of conservation laws, C. R. Math. Acad. Sci. Paris 335 (2002), 839-845.
    • (2002) C. R. Math. Acad. Sci. Paris , vol.335 , pp. 839-845
    • Bardos, C.1    Pironneau, O.2
  • 10
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3D Euler equations
    • J. T. Beale, T. Kato, A.J. Majda: Remarks on the breakdown of smooth solutions for the 3D Euler equations, Commun. Math. Phys. 1994 (1984), 61-66.
    • (1984) Commun. Math. Phys , vol.1994 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.J.3
  • 11
    • 0000411415 scopus 로고    scopus 로고
    • The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules
    • A. Bobylev. The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules, Sov. Sci. Rev. C. Math. Phys. 7 (1998), 111-233.
    • (1998) Sov. Sci. Rev. C. Math. Phys , vol.7 , pp. 111-233
    • Bobylev, A.1
  • 12
    • 0033074299 scopus 로고    scopus 로고
    • On the rate of entropy production for the Boltzmann equation
    • A. Bobylev, C. Gercignani. On the rate of entropy production for the Boltzmann equation, J. Statis. Phys 94 (1999), 603-618.
    • (1999) J. Statis. Phys , vol.94 , pp. 603-618
    • Bobylev, A.1    Gercignani, C.2
  • 15
    • 0032220965 scopus 로고    scopus 로고
    • A proof of the smoothing properties of the positive part of Boltzmann's kernel
    • F. Bouchut, L. Desvillettes. A proof of the smoothing properties of the positive part of Boltzmann's kernel, Rev. Mat. Iberoamericana 14 (1998), 47-61.
    • (1998) Rev. Mat. Iberoamericana , vol.14 , pp. 47-61
    • Bouchut, F.1    Desvillettes, L.2
  • 17
    • 0000373558 scopus 로고    scopus 로고
    • Convergence of the Vlasov-Poisson system to the incompressible Euler equations
    • Y. Brenier. Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations 25 (2000), 737-754.
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 737-754
    • Brenier, Y.1
  • 18
    • 34247463858 scopus 로고
    • The semigroup generated by 2 × 2 conservation laws
    • A. Bressan, R. Colombo. The semigroup generated by 2 × 2 conservation laws, Arch. Rational Mech. Anal. 133 (1995), 1-75.
    • (1995) Arch. Rational Mech. Anal , vol.133 , pp. 1-75
    • Bressan, A.1    Colombo, R.2
  • 19
    • 23744450066 scopus 로고    scopus 로고
    • Vanishing viscosity solutions of nonlinear hyperbolic systems
    • A. Bressan, S. Bianchini. Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math. 161 (2005), 223-342.
    • (2005) Ann. of Math , vol.161 , pp. 223-342
    • Bressan, A.1    Bianchini, S.2
  • 21
    • 84934248450 scopus 로고
    • Continuity and compactness of measures
    • J. Brooks, R. Chacon. Continuity and compactness of measures. Adv. in Math. 37 (1980), 6-26.
    • (1980) Adv. in Math , vol.37 , pp. 6-26
    • Brooks, J.1    Chacon, R.2
  • 22
    • 84990576577 scopus 로고
    • Partial regularity of suitable weak solutions of the Navier-Stokes equations
    • L. Caffarelli, R. Kohn, L. Nirenberg. Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831.
    • (1982) Comm. Pure Appl. Math , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 23
    • 34250258536 scopus 로고    scopus 로고
    • R.E. Caflisch: The Boltzmann equation with a soft potential. I. Linear, spatially-homogeneous, Commun. Math. Phys. 74 (1980), 71-95.
    • R.E. Caflisch: The Boltzmann equation with a soft potential. I. Linear, spatially-homogeneous, Commun. Math. Phys. 74 (1980), 71-95.
  • 24
    • 84980175331 scopus 로고
    • The fluid dynamic limit of the nonlinear Boltzmann equation
    • R.E. Caflisch: The fluid dynamic limit of the nonlinear Boltzmann equation, Comm. on Pure and Appl. Math. 33 (1980), 651-666.
    • (1980) Comm. on Pure and Appl. Math , vol.33 , pp. 651-666
    • Caflisch, R.E.1
  • 26
    • 85009428272 scopus 로고    scopus 로고
    • F. Castella, B. Perthame. Estimations de Strichartz pour les équations de transport cinétique, C. R. Acad. Sci. Paris Sr. I Math. 322 (1996), 535-540.
    • F. Castella, B. Perthame. Estimations de Strichartz pour les équations de transport cinétique, C. R. Acad. Sci. Paris Sr. I Math. 322 (1996), 535-540.
  • 27
    • 0003312241 scopus 로고
    • Fluides parfaits incompressibles [Incompressible perfect fluids]
    • J.-Y. Chemin. Fluides parfaits incompressibles [Incompressible perfect fluids], Astérisque 230, 1995.
    • (1995) Astérisque , vol.230
    • Chemin, J.-Y.1
  • 29
    • 33646540305 scopus 로고    scopus 로고
    • Global weak solutions of the Boltzmann equation
    • C. Cercignani. Global weak solutions of the Boltzmann equation, J. Stat. Phys. 118 (2005), 333-342.
    • (2005) J. Stat. Phys , vol.118 , pp. 333-342
    • Cercignani, C.1
  • 30
    • 18844472351 scopus 로고    scopus 로고
    • Global weak solutions to the Boltzmann equation in a slab with diffusive boundary conditions
    • C Cercignani, R. Illner. Global weak solutions to the Boltzmann equation in a slab with diffusive boundary conditions, Arch. Rational Mech. Anal. 134 (1996), 1-16.
    • (1996) Arch. Rational Mech. Anal , vol.134 , pp. 1-16
    • Cercignani, C.1    Illner, R.2
  • 32
    • 0002629777 scopus 로고
    • Théorèmes de traces pour des espaces de fonctions de la neutronique
    • M. Cessenat. Théorèmes de traces pour des espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris 300 (1985), 89-92.
    • (1985) C. R. Acad. Sci. Paris , vol.300 , pp. 89-92
    • Cessenat, M.1
  • 36
    • 0013425945 scopus 로고    scopus 로고
    • Hyperbolic conservation laws in continuum physics
    • Springer-Verlag, Berlin
    • CM. Dafermos: "Hyperbolic conservation laws in continuum physics." Grundlehren der Mathematischen Wissenschaften 325, Springer-Verlag, Berlin, 2000.
    • (2000) Grundlehren der Mathematischen Wissenschaften , vol.325
    • Dafermos, C.M.1
  • 37
    • 0039300616 scopus 로고
    • Généralisation formelle du théorème H en présence de parois
    • Darrozès, J.S.; Guiraud, J.P., Généralisation formelle du théorème H en présence de parois, C.R. Acad. Sci. Paris 262 (1966), 368-371.
    • (1966) C.R. Acad. Sci. Paris , vol.262 , pp. 368-371
    • Darrozès, J.S.1    Guiraud, J.P.2
  • 39
    • 65349178544 scopus 로고    scopus 로고
    • Notes on hyperbolic systems of conservation laws and transport equations
    • Preprint
    • C. De Lellis: Notes on hyperbolic systems of conservation laws and transport equations, Preprint (2006).
    • (2006)
    • De Lellis, C.1
  • 40
    • 67650760402 scopus 로고    scopus 로고
    • On admissibility criteria for weak solutions of the Euler equations
    • Preprint
    • C. De Leilis, L. Székelyhidi: On admissibility criteria for weak solutions of the Euler equations, Preprint (2008).
    • (2008)
    • De Leilis, C.1    Székelyhidi, L.2
  • 41
    • 84968509708 scopus 로고
    • Existence de nappes de tourbillon en dimension deux [Existence of vortex sheets in dimension two]
    • J.-M. Delort. Existence de nappes de tourbillon en dimension deux [Existence of vortex sheets in dimension two], J. Amer. Math. Soc. 4 (1991), 553-586.
    • (1991) J. Amer. Math. Soc , vol.4 , pp. 553-586
    • Delort, J.-M.1
  • 42
    • 84990591606 scopus 로고
    • Incompressible Navier-Stokes and Euler Limits of the Boltzmann Equation
    • A. DeMasi, R. Esposito, J. Lebowitz, Incompressible Navier-Stokes and Euler Limits of the Boltzmann Equation, Comm Pure Appl. Math. 42 (1990), 1189-1214.
    • (1990) Comm Pure Appl. Math , vol.42 , pp. 1189-1214
    • DeMasi, A.1    Esposito, R.2    Lebowitz, J.3
  • 43
    • 0040348944 scopus 로고
    • A remark concerning the Chapman-Enskog asymptotics
    • Advances in kinetic theory and computing, B. Perthame ed, World Sci. Publishing, River Edge, NJ
    • L. Desvillet tes, F. Golse, A remark concerning the Chapman-Enskog asymptotics, in "Advances in kinetic theory and computing", B. Perthame ed., 191-203, Ser. Adv. Math. Appl. Sci., 22, World Sci. Publishing, River Edge, NJ, 1994.
    • (1994) Ser. Adv. Math. Appl. Sci , vol.22 , pp. 191-203
    • Desvillet tes, L.1    Golse, F.2
  • 44
    • 0001089576 scopus 로고
    • On the Cauchy problem for the Boltzmann equation: Global existence and weak stability results
    • R.J. DiPerna, P.-L. Lions: On the Cauchy problem for the Boltzmann equation: global existence and weak stability results, Ann. of Math. 130 (1990), 321-366.
    • (1990) Ann. of Math , vol.130 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.-L.2
  • 45
    • 0010032457 scopus 로고
    • The first and second fluid approximations to the linearized Boltzmann equation
    • R. Ellis & M. Pinsky. The first and second fluid approximations to the linearized Boltzmann equation,. J. Math. Pures Appl. 54 (1975), 125-156.
    • (1975) J. Math. Pures Appl , vol.54 , pp. 125-156
    • Ellis, R.1    Pinsky, M.2
  • 46
    • 0030568043 scopus 로고    scopus 로고
    • Navier-Stokes equations for stochastic particle systems on the lattice
    • R. Esposito, R. Marra, H.T. Yau. Navier-Stokes equations for stochastic particle systems on the lattice. Comm. Math. Phys. 182 (1996), 395-456.
    • (1996) Comm. Math. Phys , vol.182 , pp. 395-456
    • Esposito, R.1    Marra, R.2    Yau, H.T.3
  • 47
    • 33748644085 scopus 로고    scopus 로고
    • Existence de chocs faibles pour des systmes quasilinaires hyperboliques multidimensionnels [Existence of weak shocks for multidimensional hyperbolic quasilinear systems]
    • J. Francheteau & G. Métivier: Existence de chocs faibles pour des systmes quasilinaires hyperboliques multidimensionnels [Existence of weak shocks for multidimensional hyperbolic quasilinear systems], Astérisque 268 (2000).
    • (2000) Astérisque , vol.268
    • Francheteau, J.1    Métivier, G.2
  • 48
    • 34250947482 scopus 로고
    • On the Navier-Stokes initial value problem. I
    • H. Fujita, T. Kalo. On the Navier-Stokes initial value problem. I. Arch. Rational Mech. Anal. 16 (1964), 269-315.
    • (1964) Arch. Rational Mech. Anal , vol.16 , pp. 269-315
    • Fujita, H.1    Kalo, T.2
  • 50
    • 0036627614 scopus 로고    scopus 로고
    • Arch. Rat. Mech. Anal. 163 (2002), 209-258.
    • (2002) Arch. Rat. Mech. Anal , vol.163 , pp. 209-258
  • 51
    • 84981759861 scopus 로고
    • Solutions in the large for nonlinear hyperbolic systems of equations
    • J. Glimm: Solutions in the large for nonlinear hyperbolic systems of equations, Comm. on Pure and Appl. Math. 18 (1965), 697-715.
    • (1965) Comm. on Pure and Appl. Math , vol.18 , pp. 697-715
    • Glimm, J.1
  • 52
    • 0036108339 scopus 로고    scopus 로고
    • The Stokes-Fourier and Acoustic Limits for the Boltzmann Equation
    • F. Golse, D. Levermore. The Stokes-Fourier and Acoustic Limits for the Boltzmann Equation, Comm. on Pure and Appl. Math. 55 (2002), 336-393.
    • (2002) Comm. on Pure and Appl. Math , vol.55 , pp. 336-393
    • Golse, F.1    Levermore, D.2
  • 54
    • 45549114712 scopus 로고
    • Regularity of the moments of the solution of a transport equation
    • F. Golse, P.-L. Lions, B. Perthame, R. Sentis: Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988), 110-125.
    • (1988) J. Funct. Anal , vol.76 , pp. 110-125
    • Golse, F.1    Lions, P.-L.2    Perthame, B.3    Sentis, R.4
  • 55
    • 0742323595 scopus 로고    scopus 로고
    • The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
    • F. Golse, L. Saint-Raymond. The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels, Invent. Math. 155 (2004), no. 1, 81-161.
    • (2004) Invent. Math , vol.155 , Issue.1 , pp. 81-161
    • Golse, F.1    Saint-Raymond, L.2
  • 59
    • 65349186836 scopus 로고    scopus 로고
    • Hydrodynamic limits for the Boltzmann equation
    • F. Golse, L. Saint-Raymond. Hydrodynamic limits for the Boltzmann equation, Riv. Mat. Univ. Parma 4 (2005), 1-144.
    • (2005) Riv. Mat. Univ. Parma , vol.4 , pp. 1-144
    • Golse, F.1    Saint-Raymond, L.2
  • 62
    • 0034403210 scopus 로고    scopus 로고
    • On the nonlinear instability of Euler and Prandtl equations
    • E. Grenier. On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000), 1067-1091.
    • (2000) Comm. Pure Appl. Math , vol.53 , pp. 1067-1091
    • Grenier, E.1
  • 63
    • 8844227476 scopus 로고    scopus 로고
    • The Boltzmann equation in the whole space
    • Y. Guo. The Boltzmann equation in the whole space, Indiana Univ. Math. J. 53 (2004), 1081-1094.
    • (2004) Indiana Univ. Math. J , vol.53 , pp. 1081-1094
    • Guo, Y.1
  • 64
    • 46749108210 scopus 로고
    • Problèmes aux limites pour l'équation de Boltzmann: Existence globale de solutions [Boundary value problems for the Boltzmann equation: global existence of solutions]
    • K. Harndache: Problèmes aux limites pour l'équation de Boltzmann: existence globale de solutions [Boundary value problems for the Boltzmann equation: global existence of solutions], Comm. Partial Differential Equations 13 (1988), 813-845.
    • (1988) Comm. Partial Differential Equations , vol.13 , pp. 813-845
    • Harndache, K.1
  • 66
    • 0001243518 scopus 로고
    • Begründung der kinetischen Gastheorie
    • D. Hilbert. Begründung der kinetischen Gastheorie Math. Ann. 72 (1912), 562-577.
    • (1912) Math. Ann , vol.72 , pp. 562-577
    • Hilbert, D.1
  • 67
    • 0023501738 scopus 로고
    • On the initial layer and the existence theorem for the nonlinear Boltzmann equation
    • M. Lachowicz, On the initial layer and the existence theorem for the nonlinear Boltzmann equation. Math. Methods Appl. Sci. 9 (1987), 342-366.
    • (1987) Math. Methods Appl. Sci , vol.9 , pp. 342-366
    • Lachowicz, M.1
  • 68
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation laws. II
    • P.D. Lax: Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537-566.
    • (1957) Comm. Pure Appl. Math , vol.10 , pp. 537-566
    • Lax, P.D.1
  • 69
    • 0031184915 scopus 로고    scopus 로고
    • Fluctuation-dissipation equation of asymmetric simple exclusion processes
    • G. Landim, H.T. Yau. Fluctuation-dissipation equation of asymmetric simple exclusion processes. Probab. Theory Related Fields 108 (1997), 321-356.
    • (1997) Probab. Theory Related Fields , vol.108 , pp. 321-356
    • Landim, G.1    Yau, H.T.2
  • 70
    • 0001518823 scopus 로고
    • Time evolution of large classical systems Lect
    • J. Moser ed, Springer Verlag
    • O.E. Lanford, Time evolution of large classical systems Lect. Notes in Physics 38, J. Moser ed., 1-111, Springer Verlag (1975).
    • (1975) Notes in Physics , vol.38 , pp. 1-111
    • Lanford, O.E.1
  • 71
    • 0003068173 scopus 로고
    • Etude de diverses équations intégrales non linéaires et quelques problèmes que pose l'hydridynamique
    • J. Leray. Etude de diverses équations intégrales non linéaires et quelques problèmes que pose l'hydridynamique, J. Math. Pures Appl. 9 (1933), 1-82.
    • (1933) J. Math. Pures Appl , vol.9 , pp. 1-82
    • Leray, J.1
  • 72
    • 34250952136 scopus 로고
    • Über einige Existenz Problem der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flüssikeiten und, die Helmholtzschen Wirbelsalitze
    • L. Lichtenstein: Über einige Existenz Problem der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flüssikeiten und, die Helmholtzschen Wirbelsalitze, Mat. Zeit. Phys. 23 (1925),
    • (1925) Mat. Zeit. Phys , vol.23
    • Lichtenstein, L.1
  • 73
    • 85009403693 scopus 로고    scopus 로고
    • 89154; 28 1927
    • 89154; 28 (1927),
  • 74
    • 85009375475 scopus 로고    scopus 로고
    • 193323; 32 1930, 608
    • 193323; 32 (1930), 608.
  • 76
    • 0042249038 scopus 로고
    • Conditions at infinity for Boltzmann's equation
    • P.-L. Lions, Conditions at infinity for Boltzmann's equation, Comm. Partial Differential Equations 19 (1994), 335-367.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 335-367
    • Lions, P.-L.1
  • 77
    • 85009403696 scopus 로고    scopus 로고
    • P.-L. Lions: Mathematical Topics in Fluid Mechanics, 1: Incompressible Models, The Clarendon Press, Oxford University Press, New York, 1996.
    • P.-L. Lions: "Mathematical Topics in Fluid Mechanics, Vol. 1: Incompressible Models", The Clarendon Press, Oxford University Press, New York, 1996.
  • 78
    • 0035616508 scopus 로고    scopus 로고
    • From Boltzmann Equation to the Navier-Stokes and Euler Equations I
    • P.-L. Lions, N. Masmoudi: From Boltzmann Equation to the Navier-Stokes and Euler Equations I, Archive Rat. Mech. & Anal. 158 (2001), 173-193.
    • (2001) Archive Rat. Mech. & Anal , vol.158 , pp. 173-193
    • Lions, P.-L.1    Masmoudi, N.2
  • 79
    • 0035614842 scopus 로고    scopus 로고
    • From Boltzmann Equation to the Navier-Stokes and Euler Equations II
    • P.-L. Lions, N. Masmoudi: From Boltzmann Equation to the Navier-Stokes and Euler Equations II, Archive Rat. Mech. & Anal. 158 (2001), 195-211.
    • (2001) Archive Rat. Mech. & Anal , vol.158 , pp. 195-211
    • Lions, P.-L.1    Masmoudi, N.2
  • 81
    • 0017416618 scopus 로고
    • Solutions in the large for the equations of nonisentropic gas dynamics
    • T. P. Liu. Solutions in the large for the equations of nonisentropic gas dynamics, Indiana Univ. Math. J. 26 (1977), 147-177.
    • (1977) Indiana Univ. Math. J , vol.26 , pp. 147-177
    • Liu, T.P.1
  • 82
    • 1842591085 scopus 로고    scopus 로고
    • Boltzmann equation: Micro-macro decompositions and positivity of shock profiles
    • T.-P. Liu, S.-H. Yu: Boltzmann equation: micro-macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004), 133-179.
    • (2004) Comm. Math. Phys , vol.246 , pp. 133-179
    • Liu, T.-P.1    Yu, S.-H.2
  • 83
    • 0346498040 scopus 로고    scopus 로고
    • Energy method for Boltzmann equation
    • T.-P. Liu, T. Yang, S.-H. Yu: Energy method for Boltzmann equation, Phys. D 188 (2004), 178-192.
    • (2004) Phys. D , vol.188 , pp. 178-192
    • Liu, T.-P.1    Yang, T.2    Yu, S.-H.3
  • 85
    • 0042843384 scopus 로고    scopus 로고
    • N. Masmoudi, L. Saint-Raymond. From the Boltzmann equation to the Stokes-Fourier system in a bounded domain, Comm. Pure Appl. Math., 56 (2003), 1263-1293.
    • N. Masmoudi, L. Saint-Raymond. From the Boltzmann equation to the Stokes-Fourier system in a bounded domain, Comm. Pure Appl. Math., 56 (2003), 1263-1293.
  • 86
    • 65349099703 scopus 로고    scopus 로고
    • Existence of semilinear relaxation shocks
    • Preprint
    • G. Métivier, K. Zumbrun. Existence of semilinear relaxation shocks. Preprint 2008.
    • (2008)
    • Métivier, G.1    Zumbrun, K.2
  • 87
    • 0034348887 scopus 로고    scopus 로고
    • On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
    • S. Mischler. On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system, Comm. Math. Phys. 210 (2000), 447-466.
    • (2000) Comm. Math. Phys , vol.210 , pp. 447-466
    • Mischler, S.1
  • 89
    • 84980085582 scopus 로고
    • On the derivation of the equations of hydrodynamics from Statistical Mechanics
    • C. B. Morrey. On the derivation of the equations of hydrodynamics from Statistical Mechanics, Commun. Pure Appl. Math., 8 (1955), 279-290.
    • (1955) Commun. Pure Appl. Math , vol.8 , pp. 279-290
    • Morrey, C.B.1
  • 90
    • 29144473644 scopus 로고    scopus 로고
    • C. Mouhot. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials, (Jomm. Math. Phys. 261 (2006), 629-672.
    • C. Mouhot. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials, (Jomm. Math. Phys. 261 (2006), 629-672.
  • 91
    • 0000464203 scopus 로고
    • Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
    • T. Nishida. Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation. Comm. Math. Phys. 61 (1978), 119-148.
    • (1978) Comm. Math. Phys , vol.61 , pp. 119-148
    • Nishida, T.1
  • 92
    • 21344483632 scopus 로고
    • Hydrodynamical limit for a Hamiltonian system with weak noise
    • S. Olla, S. Varadhan, H. Yau, Hydrodynamical limit for a Hamiltonian system with weak noise, Commun. Math. Phys. 155 (1993), 523-560.
    • (1993) Commun. Math. Phys , vol.155 , pp. 523-560
    • Olla, S.1    Varadhan, S.2    Yau, H.3
  • 93
    • 0010080132 scopus 로고    scopus 로고
    • Introduction to the collision models in Boltzmann's theory
    • P.-A. Raviart ed, Masson, Paris
    • B. Perthame: Introduction to the collision models in Boltzmann's theory, in "Modeling of Collisions", P.-A. Raviart ed., Masson, Paris, 1997.
    • (1997) Modeling of Collisions
    • Perthame, B.1
  • 94
    • 0032334703 scopus 로고    scopus 로고
    • Lattice gases, large deviations, and the incompressible Navier-Stokes equations
    • J. Quastel and H.-T. Yau, Lattice gases, large deviations, and the incompressible Navier-Stokes equations, Ann. of Math. 148 (1998), 51-108.
    • (1998) Ann. of Math , vol.148 , pp. 51-108
    • Quastel, J.1    Yau, H.-T.2
  • 95
    • 0038030902 scopus 로고    scopus 로고
    • From the BGK model to the Navier-Stokes equations
    • L. Saint-Raymond: From the BGK model to the Navier-Stokes equations, Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), 271-317.
    • (2003) Ann. Sci. Ecole Norm. Sup. (4) , vol.36 , pp. 271-317
    • Saint-Raymond, L.1
  • 96
    • 0036331819 scopus 로고    scopus 로고
    • Du modèle BGK de l'équation de Boltzmann aux équations d'Evier des fluides incompressibles
    • L. Saint-Raymond: Du modèle BGK de l'équation de Boltzmann aux équations d'Evier des fluides incompressibles, Bull. Sci. Math. 126 (2002), 493-506.
    • (2002) Bull. Sci. Math , vol.126 , pp. 493-506
    • Saint-Raymond, L.1
  • 97
    • 0037237744 scopus 로고    scopus 로고
    • Convergence of solutions to the Boltzmann equation in the incompressible Euler limit
    • L. Saint-Raymond: Convergence of solutions to the Boltzmann equation in the incompressible Euler limit, Arch. Ration. Mech. Anal. 166 (2003), 47-80.
    • (2003) Arch. Ration. Mech. Anal , vol.166 , pp. 47-80
    • Saint-Raymond, L.1
  • 98
    • 67349123434 scopus 로고    scopus 로고
    • L. Saint-Raymond: Hydrodynamic Urn/its: some improvements of the relative entropy method, Ann. Iust. H. Poincaré, to appear, 2008. doi:10.1016/j.anihpc.2008.01.001.
    • L. Saint-Raymond: Hydrodynamic Urn/its: some improvements of the relative entropy method, Ann. Iust. H. Poincaré, to appear, 2008. doi:10.1016/j.anihpc.2008.01.001.
  • 99
    • 43949155251 scopus 로고
    • Fast singular limits of hyperbolic PDEs
    • S. Schochet. Fast singular limits of hyperbolic PDEs, J. Differential Equations 114 (1994), 476-512.
    • (1994) J. Differential Equations , vol.114 , pp. 476-512
    • Schochet, S.1
  • 102
    • 0000169262 scopus 로고
    • On the interior regularity of weak solutions of the Navier-Stokes equations
    • J. Serrin: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 9 (1962), 187-195.
    • (1962) Arch. Rational Mech. Anal , vol.9 , pp. 187-195
    • Serrin, J.1
  • 103
    • 0001628249 scopus 로고
    • Formation of Singularities in 3D Compressible Fluids
    • T. Sideris: Formation of Singularities in 3D Compressible Fluids, Commun. Math. Phys. 101 (1985), 475-485.
    • (1985) Commun. Math. Phys , vol.101 , pp. 475-485
    • Sideris, T.1
  • 104
    • 0003233281 scopus 로고
    • Shock waves and reaction-diffusion equations
    • Springer-Verlag, New York-Berlin
    • J. Smoller: "Shock waves and reaction-diffusion equations." Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, New York-Berlin, 1983.
    • (1983) Grundlehren der Mathematischen Wissenschaften
    • Smoller, J.1
  • 105
    • 0003887517 scopus 로고
    • Navier-Stokes equations. Theory and numerical analysis
    • North-Holland Publishing Co, Amsterdam-New York-Oxford
    • R. Ternam: "Navier-Stokes equations. Theory and numerical analysis." Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977.
    • (1977) Studies in Mathematics and its Applications
    • Ternam, R.1
  • 106
    • 0000824099 scopus 로고
    • On the existence of global solutions of a mixed problem for the nonlinear Boltzmann equation
    • S. Ukai. On the existence of global solutions of a mixed problem for the nonlinear Boltzmann equation, Proc. of the Japan Acad. 50 (1974), 179-184.
    • (1974) Proc. of the Japan Acad , vol.50 , pp. 179-184
    • Ukai, S.1
  • 107
    • 0000106013 scopus 로고
    • Eigenvalues of the neutron transport operator for a homogeneous finite moderator
    • S. Ukai: Eigenvalues of the neutron transport operator for a homogeneous finite moderator, J. Math. Anal. Appl. 18 (1967), 297-314.
    • (1967) J. Math. Anal. Appl , vol.18 , pp. 297-314
    • Ukai, S.1
  • 108
    • 0000537351 scopus 로고
    • The Euler limit and initial layer of the nonlinear Boltzmann equation
    • S. Ukai, K. Asano: The Euler limit and initial layer of the nonlinear Boltzmann equation, Hokkaido Math. J. 12 (1983), 311-332.
    • (1983) Hokkaido Math. J , vol.12 , pp. 311-332
    • Ukai, S.1    Asano, K.2
  • 109
    • 67649344144 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • North-Holland, Amsterdam
    • C. Villani: "A review of mathematical topics in collisional kinetic theory." Handbook of mathematical fluid dynamics, North-Holland, Amsterdam, 2002.
    • (2002) Handbook of mathematical fluid dynamics
    • Villani, C.1
  • 111
    • 0003135582 scopus 로고
    • Relative entropy and hydrodynamics of Ginzburg-Landau models
    • H. T. Yau. Relative entropy and hydrodynamics of Ginzburg-Landau models, Lett. Math. Phys. 22 (1991), 63-80.
    • (1991) Lett. Math. Phys , vol.22 , pp. 63-80
    • Yau, H.T.1
  • 112
    • 3543018925 scopus 로고    scopus 로고
    • Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation
    • Math
    • H. T. Yau. Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation. Proceedings of the International Congress of Mathematicians, Doc. Math. 3 (1998), 193-202.
    • (1998) Proceedings of the International Congress of Mathematicians, Doc , vol.3 , pp. 193-202
    • Yau, H.T.1


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