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Volumn 206, Issue 2, 2012, Pages 367-488

From Boltzmann's Equation to the Incompressible Navier-Stokes-Fourier System with Long-Range Interactions

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EID: 84870359744     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-012-0557-9     Document Type: Article
Times cited : (30)

References (35)
  • 2
    • 79959709918 scopus 로고    scopus 로고
    • The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
    • Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential. Anal. Appl. (Singap.) 9(2), 113-134 (2011).
    • (2011) Anal. Appl. (Singap.) , vol.9 , Issue.2 , pp. 113-134
    • Alexandre, R.1    Morimoto, Y.2    Ukai, S.3    Xu, C.-J.4    Yang, T.5
  • 3
    • 84155195145 scopus 로고    scopus 로고
    • The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential
    • Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential. J. Funct. Anal. 262(3), 915-1010 (2012).
    • (2012) J. Funct. Anal. , vol.262 , Issue.3 , pp. 915-1010
    • Alexandre, R.1    Morimoto, Y.2    Ukai, S.3    Xu, C.-J.4    Yang, T.5
  • 4
    • 0036133764 scopus 로고    scopus 로고
    • On the Boltzmann equation for long-range interactions
    • Alexandre R., Villani C.: On the Boltzmann equation for long-range interactions. Comm. Pure Appl. Math. 55(1), 30-70 (2002).
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.1 , pp. 30-70
    • Alexandre, R.1    Villani, C.2
  • 7
    • 84870371908 scopus 로고    scopus 로고
    • A new approach to velocity averaging lemmas in Besov spaces
    • (submitted)
    • Arsénio, D., Masmoudi, N.: A new approach to velocity averaging lemmas in Besov spaces. J. Math. Pures Appl. (2012) (submitted).
    • (2012) J. Math. Pures Appl.
    • Arsénio, D.1    Masmoudi, N.2
  • 8
    • 84856282688 scopus 로고    scopus 로고
    • Regularity of renormalized solutions in the Boltzmann equation with long-range interactions
    • Arsénio D., Masmoudi N.: Regularity of renormalized solutions in the Boltzmann equation with long-range interactions. Comm. Pure Appl. Math. 65(4), 508-548 (2012).
    • (2012) Comm. Pure Appl. Math. , vol.65 , Issue.4 , pp. 508-548
    • Arsénio, D.1    Masmoudi, N.2
  • 9
    • 84990619144 scopus 로고
    • Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation
    • Bardos C., Golse F., Levermore C. D.: Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Comm. Pure Appl. Math. 46(5), 667-753 (1993).
    • (1993) Comm. Pure Appl. Math. , vol.46 , Issue.5 , pp. 667-753
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 12
    • 0001076950 scopus 로고
    • Fluid dynamic limits of kinetic equations. I. Formal derivations
    • Bardos C., Golse F., Levermore C. D.: Fluid dynamic limits of kinetic equations. I. Formal derivations. J. Stat. Phys. 63(1-2), 323-344 (1991).
    • (1991) J. Stat. Phys. , vol.63 , Issue.1-2 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 13
    • 0002665670 scopus 로고
    • p précisée des moyennes dans les équations de transport
    • p précisée des moyennes dans les équations de transport. Bull. Soc. Math. France 122(1), 29-76 (1994).
    • (1994) Bull. Soc. Math. France , vol.122 , Issue.1 , pp. 29-76
    • Bézard, M.1
  • 14
    • 0009886850 scopus 로고    scopus 로고
    • Kinetic equations and asymptotic theory
    • Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris, (Edited and with a foreword by Benoît Perthame and Laurent Desvillettes)
    • Bouchut, F., Golse, F., Pulvirenti, M.: Kinetic equations and asymptotic theory. In: Series in Applied Mathematics (Paris), vol. 4. Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris, 2000. (Edited and with a foreword by Benoît Perthame and Laurent Desvillettes).
    • (2000) Series in Applied Mathematics (Paris) , vol.4
    • Bouchut, F.1    Golse, F.2    Pulvirenti, M.3
  • 16
    • 0003312241 scopus 로고
    • Fluides parfaits incompressibles
    • Chemin J.-Y.: Fluides parfaits incompressibles. Astérisque 230, 177 (1995).
    • (1995) Astérisque , vol.230 , pp. 177
    • Chemin, J.-Y.1
  • 17
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: global existence and weak stability
    • DiPerna R. J., Lions P.-L.: On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. (2) 130(2), 321-366 (1989).
    • (1989) Ann. Math. (2) , vol.130 , Issue.2 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.-L.2
  • 19
    • 16744364213 scopus 로고    scopus 로고
    • The Stokes-Fourier limit for the Boltzmann equation
    • Golse F., Levermore C. D.: The Stokes-Fourier limit for the Boltzmann equation. C. R. Acad. Sci. Paris Sér. I Math. 333(2), 145-150 (2001).
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , Issue.2 , pp. 145-150
    • Golse, F.1    Levermore, C.D.2
  • 20
    • 0036108339 scopus 로고    scopus 로고
    • Stokes-Fourier and acoustic limits for the Boltzmann equation: convergence proofs
    • Golse F., Levermore C. D.: Stokes-Fourier and acoustic limits for the Boltzmann equation: convergence proofs. Comm. Pure Appl. Math. 55(3), 336-393 (2002).
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.3 , pp. 336-393
    • Golse, F.1    Levermore, C.D.2
  • 22
    • 0742323595 scopus 로고    scopus 로고
    • The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
    • Golse F., Saint-Raymond L.: The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels. Invent. Math. 155(1), 81-161 (2004).
    • (2004) Invent. Math. , vol.155 , Issue.1 , pp. 81-161
    • Golse, F.1    Saint-Raymond, L.2
  • 23
    • 64549141523 scopus 로고    scopus 로고
    • The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials
    • Golse F., Saint-Raymond L.: The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials. J. Math. Pures Appl. (9) 91(5), 508-552 (2009).
    • (2009) J. Math. Pures Appl. (9) , vol.91 , Issue.5 , pp. 508-552
    • Golse, F.1    Saint-Raymond, L.2
  • 24
    • 79953745167 scopus 로고    scopus 로고
    • Global classical solutions of the Boltzmann equation without angular cut-off
    • Gressman P. T., Strain R. M.: Global classical solutions of the Boltzmann equation without angular cut-off. J. Am. Math. Soc. 24(3), 771-847 (2011).
    • (2011) J. Am. Math. Soc. , vol.24 , Issue.3 , pp. 771-847
    • Gressman, P.T.1    Strain, R.M.2
  • 25
    • 51249193194 scopus 로고
    • Sur le mouvement d'un liquide visqueux emplissant l'espace
    • Leray J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63(1), 193-248 (1934).
    • (1934) Acta Math. , vol.63 , Issue.1 , pp. 193-248
    • Leray, J.1
  • 26
    • 77952010642 scopus 로고    scopus 로고
    • From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system
    • Levermore C. D., Masmoudi N.: From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system. Arch. Ration. Mech. Anal. 196(3), 753-809 (2010).
    • (2010) Arch. Ration. Mech. Anal. , vol.196 , Issue.3 , pp. 753-809
    • Levermore, C.D.1    Masmoudi, N.2
  • 27
    • 0001416655 scopus 로고
    • On Boltzmann and Landau equations
    • Lions P.-L.: On Boltzmann and Landau equations. Philos. Trans. R. Soc. Lond. Ser. A 346(1679), 191-204 (1994).
    • (1994) Philos. Trans. R. Soc. Lond. Ser. A , vol.346 , Issue.1679 , pp. 191-204
    • Lions, P.-L.1
  • 28
    • 0032085754 scopus 로고    scopus 로고
    • Incompressible limit for a viscous compressible fluid
    • Lions P.-L., Masmoudi N.: Incompressible limit for a viscous compressible fluid. J. Math. Pures Appl. (9) 77(6), 585-627 (1998).
    • (1998) J. Math. Pures Appl. (9) , vol.77 , Issue.6 , pp. 585-627
    • Lions, P.-L.1    Masmoudi, N.2
  • 29
    • 0035616508 scopus 로고    scopus 로고
    • From the Boltzmann equations to the equations of incompressible fluid mechanics
    • 195-211
    • Lions, P.-L., Masmoudi, N.: From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Arch. Ration. Mech. Anal. 158(3), 173-193, 195-211 (2001).
    • (2001) I, II. Arch. Ration. Mech. Anal. , vol.158 , Issue.3 , pp. 173-193
    • Lions, P.-L.1    Masmoudi, N.2
  • 30
    • 0000927020 scopus 로고    scopus 로고
    • Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire
    • Lions P.-L.: Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire. C. R. Acad. Sci. Paris Sér. I Math. 326(1), 37-41 (1998).
    • (1998) C. R. Acad. Sci. Paris Sér. I Math. , vol.326 , Issue.1 , pp. 37-41
    • Lions, P.-L.1
  • 32
    • 33748450509 scopus 로고    scopus 로고
    • Explicit coercivity estimates for the linearized Boltzmann and Landau operators
    • Mouhot C.: Explicit coercivity estimates for the linearized Boltzmann and Landau operators. Comm. Partial Diff. Equ. 31(7-9), 1321-1348 (2006).
    • (2006) Comm. Partial Diff. Equ. , vol.31 , Issue.7-9 , pp. 1321-1348
    • Mouhot, C.1
  • 33
    • 34248226318 scopus 로고    scopus 로고
    • Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
    • Mouhot C., Strain R. M.: Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff. J. Math. Pures Appl. (9) 87(5), 515-535 (2007).
    • (2007) J. Math. Pures Appl. (9) , vol.87 , Issue.5 , pp. 515-535
    • Mouhot, C.1    Strain, R.M.2
  • 34
    • 65349138242 scopus 로고    scopus 로고
    • Hydrodynamic limits of the Boltzmann equation
    • Springer, Berlin
    • Saint-Raymond L.: Hydrodynamic limits of the Boltzmann equation. Lecture Notes in Mathematics, vol. 1971. Springer, Berlin, 2009.
    • (2009) Lecture Notes in Mathematics , vol.1971
    • Saint-Raymond, L.1
  • 35
    • 67649344144 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • North-Holland, Amsterdam
    • Villani, C.: A review of mathematical topics in collisional kinetic theory. In: Handbook of Mathematical Fluid Dynamics, vol. I, pp. 71-305. North-Holland, Amsterdam, 2002.
    • (2002) Handbook of Mathematical Fluid Dynamics , vol.I , pp. 71-305
    • Villani, C.1


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