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Volumn 14, Issue 6, 2004, Pages 853-882

On the asymptotic analysis of kinetic models towards the compressible Euler and acoustic equations

Author keywords

Acoustic limit; Asymptotic theory; BGK model; Boltzmann equation; Compressible Euler; Kinetics models

Indexed keywords


EID: 7244231027     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202504003477     Document Type: Article
Times cited : (24)

References (34)
  • 1
    • 0001315807 scopus 로고
    • The classical incompressible Navier-Stokes limit of the Boltzmann equations
    • C. Bardos and S. Ukai, The classical incompressible Navier-Stokes limit of the Boltzmann equations, Math. Mod. Meth. Appl. Sci. 2 (1991) 235-257.
    • (1991) Math. Mod. Meth. Appl. Sci. , vol.2 , pp. 235-257
    • Bardos, C.1    Ukai, S.2
  • 2
    • 0001101971 scopus 로고
    • Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles
    • C. Bardos, F. Golse and D. Levermore, Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles, C. R. Acad. Sci. Paris 309 (1989) 727-732.
    • (1989) C. R. Acad. Sci. Paris , vol.309 , pp. 727-732
    • Bardos, C.1    Golse, F.2    Levermore, D.3
  • 3
    • 84990619144 scopus 로고
    • Fluid dynamic limits of kinetic equations: Convergence proofs for the Boltzmann equation
    • C. Bardos, F. Golse and D. Levermore, Fluid dynamic limits of kinetic equations: 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, D.3
  • 5
    • 0037288629 scopus 로고    scopus 로고
    • A diffusive limit for nonlinear discrete velocity models
    • A. Bellouquid, A diffusive limit for nonlinear discrete velocity models, Math. Mod. Meth. Appl. Sci. 13 (2003) 35-58.
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.13 , pp. 35-58
    • Bellouquid, A.1
  • 6
    • 0036435154 scopus 로고    scopus 로고
    • The nonlinear incompressible Navier-Stokes for the nonlinear discrete velocity models
    • A. Bellouquid, The nonlinear incompressible Navier-Stokes for the nonlinear discrete velocity models, J. Nonlinear Math. Phys. 9 (2002) 426-445.
    • (2002) J. Nonlinear Math. Phys. , vol.9 , pp. 426-445
    • Bellouquid, A.1
  • 7
    • 0037032841 scopus 로고    scopus 로고
    • From microscopic to macroscopic models: Asymptotic analysis of the Broadwell towards the wave equation
    • A. Bellouquid, From microscopic to macroscopic models: Asymptotic analysis of the Broadwell towards the wave equation, Math. Comp, Modelling 36 (2002) 1169-1181.
    • (2002) Math. Comp, Modelling , vol.36 , pp. 1169-1181
    • Bellouquid, A.1
  • 8
    • 0033248866 scopus 로고    scopus 로고
    • The hydrodynamical limit of the nonlinear Boltzmann equation
    • A. Bellouquid, The hydrodynamical limit of the nonlinear Boltzmann equation, Tranp. Theor. Statist. Phys. 28 (1999) 25-57.
    • (1999) Tranp. Theor. Statist. Phys. , vol.28 , pp. 25-57
    • Bellouquid, A.1
  • 9
    • 0038374761 scopus 로고    scopus 로고
    • Global existence and large time behavior for BGK model for a gas with non constant cross section
    • A. Bellouquid, Global existence and large time behavior for BGK model for a gas with non constant cross section, Tranp. Theor. Statist. Phys. 32 (2003) 157-184.
    • (2003) Tranp. Theor. Statist. Phys. , vol.32 , pp. 157-184
    • Bellouquid, A.1
  • 10
    • 26344468007 scopus 로고
    • A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems
    • P. L. Bhatnagar, E. P. Gross and A. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94 (1954) 511.
    • (1954) Phys. Rev. , vol.94 , pp. 511
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, A.3
  • 11
    • 0000229982 scopus 로고
    • Weitere studien uber das warmegleichgewicht unter gas-molekulen, Sitzungs
    • L. Boltzmann, Weitere studien uber das warmegleichgewicht unter gas-molekulen, Sitzungs, Akad. Wiss. Wein 66 (1872) 275-370; English: Further studies on the thermal equilibrium of gas molecules, in Kinetic Theory 2, ed. S. G. Brush (Pergamon Press, 1966), pp. 88-174.
    • (1872) Akad. Wiss. Wein , vol.66 , pp. 275-370
    • Boltzmann, L.1
  • 12
    • 0011567818 scopus 로고
    • Further studies on the thermal equilibrium of gas molecules
    • English: Pergamon Press
    • L. Boltzmann, Weitere studien uber das warmegleichgewicht unter gas-molekulen, Sitzungs, Akad. Wiss. Wein 66 (1872) 275-370; English: Further studies on the thermal equilibrium of gas molecules, in Kinetic Theory 2, ed. S. G. Brush (Pergamon Press, 1966), pp. 88-174.
    • (1966) Kinetic Theory , vol.2 , pp. 88-174
    • Brush, S.G.1
  • 13
    • 0035605221 scopus 로고    scopus 로고
    • High field limit of the Vlasov-Poisson-Fokker-Plank system: A comparison of different perturbation methods
    • L. Bonilla and J. Soler, High field limit of the Vlasov-Poisson-Fokker- Plank system: A comparison of different perturbation methods, Math. Mod. Meth. Appl. Sci. 11 (2001) 1457-1468.
    • (2001) Math. Mod. Meth. Appl. Sci. , vol.11 , pp. 1457-1468
    • Bonilla, L.1    Soler, J.2
  • 14
    • 84980175331 scopus 로고
    • The fluid dynamic limit of the nonlinear Boltzmann equation
    • R. Caflish, The fluid dynamic limit of the nonlinear Boltzmann equation, Comm. Pure Appl. Math. 33 (1980) 651-666.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 651-666
    • Caflish, R.1
  • 15
    • 84980139661 scopus 로고
    • The fluid-dynamical limit of a nonlinear model Boltzmann equation
    • R. Caflish and G. Papanicolaou, The fluid-dynamical limit of a nonlinear model Boltzmann equation, Comm. Pure Appl. Math. 32 (1979) 589-616.
    • (1979) Comm. Pure Appl. Math. , vol.32 , pp. 589-616
    • Caflish, R.1    Papanicolaou, G.2
  • 17
    • 84990591606 scopus 로고
    • Incompressible Navier-Stokes and Euler limits of the Boltzmann equation
    • A. De Masi, R. Esposito and J. L. Lebowitz, Incompressible Navier-Stokes and Euler limits of the Boltzmann equation, Comm. Pure Appl. Math. 42 (1989) 321-366.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 321-366
    • De Masi, A.1    Esposito, R.2    Lebowitz, J.L.3
  • 18
    • 0010032457 scopus 로고
    • The first and second fluid approximation to the linearized Boltzmann equation
    • R. S. Ellis and M. Pinsky, The first and second fluid approximation 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.S.1    Pinsky, M.2
  • 19
    • 0038407473 scopus 로고    scopus 로고
    • The Vlasov-Poisson system with strong magnetic field in quasineutral regime
    • F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with strong magnetic field in quasineutral regime, Math. Mod. Meth. Appl. Sci. 13 (2003) 661-714.
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.13 , pp. 661-714
    • Golse, F.1    Saint-Raymond, L.2
  • 20
    • 0036108339 scopus 로고    scopus 로고
    • Stokes-Fourier and acoustic Limits for the Boltzmann equation: Convergence proofs
    • F. Golse and D. Levermore, Stokes-Fourier and acoustic Limits for the Boltzmann equation: Convergence proofs, Comm. Pure Appl. Math. 55 (2002) 336-393.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 336-393
    • Golse, F.1    Levermore, D.2
  • 22
    • 0037289101 scopus 로고    scopus 로고
    • Mean-Field approximation of quantum systems and classical limit
    • S. Graffi, A. Martinez and M. Pulvirenti, Mean-Field approximation of quantum systems and classical limit, Math. Mod. Meth. Appl. Sci. 13 (2003) 59-73.
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.13 , pp. 59-73
    • Graffi, S.1    Martinez, A.2    Pulvirenti, M.3
  • 23
    • 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. Meth. Appl. Sci. 9 (1987) 342-366.
    • (1987) Math. Meth. Appl. Sci. , vol.9 , pp. 342-366
    • Lachowicz, M.1
  • 24
    • 7244243350 scopus 로고
    • On the Enskog equation and its hydrodynamic limit
    • Kinetic Theory and Hyperbolic Systems, eds. V. Boffi, F. Bambi and G. Toscani, World Scientific
    • M. Lachowicz, On the Enskog equation and its hydrodynamic limit, Kinetic Theory and Hyperbolic Systems, eds. V. Boffi, F. Bambi and G. Toscani, Advances in Mathematics for Applied Sciences, Vol. 9 (World Scientific, 1992), pp. 159-165.
    • (1992) Advances in Mathematics for Applied Sciences , vol.9 , pp. 159-165
    • Lachowicz, M.1
  • 25
    • 0035616508 scopus 로고    scopus 로고
    • From Boltzmann equation to the equation of incompressible fluid mechanics
    • P. L. Lions and N. Masmoudi, From Boltzmann equation to the equation of incompressible fluid mechanics, Arch. Rational. Mech. Anal. 158 (2001) 173-193.
    • (2001) Arch. Rational. Mech. Anal. , vol.158 , pp. 173-193
    • Lions, P.L.1    Masmoudi, N.2
  • 27
    • 0000464203 scopus 로고
    • Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the incompressible Euler equation
    • T. Nishida, Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the incompressible Euler equation, Comm. Math. Phys. 61 (1978) 119-148.
    • (1978) Comm. Math. Phys. , vol.61 , pp. 119-148
    • Nishida, T.1
  • 28
    • 84972513394 scopus 로고
    • A note on a theorem of Nirenberg
    • T. Nishida, A note on a theorem of Nirenberg, J. Diff. Geom. 12 (1979) 629-633.
    • (1979) J. Diff. Geom. , vol.12 , pp. 629-633
    • Nishida, T.1
  • 29
    • 84972536320 scopus 로고
    • An abstract form of the nonlinear Cauchy-Kowaleski theorem
    • L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowaleski theorem, J. Diff. Geom. 6 (1972) 561-576.
    • (1972) J. Diff. Geom. , vol.6 , pp. 561-576
    • Nirenberg, L.1
  • 30
    • 0001168246 scopus 로고
    • A nonlinear Cauchy problem in a scale of Banach spaces
    • L. V. Ovsjannikov, A nonlinear Cauchy problem in a scale of Banach spaces, Dokl. Akad. Nauk SSSR. 200 (1971) 789-792.
    • (1971) Dokl. Akad. Nauk SSSR , vol.200 , pp. 789-792
    • Ovsjannikov, L.V.1
  • 31
    • 0034413686 scopus 로고    scopus 로고
    • Parabolic limit and stability of the Vlasov-Fokker-Planck system
    • F. Poupaud and J. Soler, Parabolic limit and stability of the Vlasov-Fokker-Planck system, Math. Mod. Meth. Appl. Sci. 10 (2000) 1027-1045.
    • (2000) Math. Mod. Meth. Appl. Sci. , vol.10 , pp. 1027-1045
    • Poupaud, F.1    Soler, J.2
  • 32
    • 0034364359 scopus 로고    scopus 로고
    • The gyrokinetic approximation for the Vlasov-Poisson system
    • L. Saint-Raymond, The gyrokinetic approximation for the Vlasov-Poisson system, Math. Mod. Meth. Appl. Sci. 10 (2000) 1305-1332.
    • (2000) Math. Mod. Meth. Appl. Sci. , vol.10 , pp. 1305-1332
    • Saint-Raymond, L.1
  • 33
    • 0001628249 scopus 로고
    • Formation of singularities in three dimensional compressible fluids
    • T. Sideris, Formation of singularities in three dimensional compressible fluids, Comm. Math. Phys. 101 (1985) 475-485.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 475-485
    • Sideris, T.1
  • 34
    • 0000537351 scopus 로고
    • The Euler limit and initial layer of the nonlinear Boltzmann equation
    • S. Ukai and 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.