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Volumn 99, Issue 3-4, 2000, Pages 993-1019

On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model

Author keywords

Boltzmann asymptotics; Boundary layer; Hydrodynamic limit; Maxwellian limit; Milne problem; Stationary gas kinetics; Weak methods

Indexed keywords


EID: 0034178387     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018655815285     Document Type: Article
Times cited : (21)

References (32)
  • 2
    • 0032355549 scopus 로고    scopus 로고
    • A condensation-evaporation problem
    • L. Arkeryd and A. Nouri, A condensation-evaporation problem, SIAM J. Math. Anal. 29:30-47 (1998).
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 30-47
    • Arkeryd, L.1    Nouri, A.2
  • 4
    • 0001962775 scopus 로고    scopus 로고
    • The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces
    • L. Arkeryd and A. Nouri, The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces, Ann. Scuola Norm. Sup. Pisa 27:533-556 (1998).
    • (1998) Ann. Scuola Norm. Sup. Pisa , vol.27 , pp. 533-556
    • Arkeryd, L.1    Nouri, A.2
  • 6
    • 0000212984 scopus 로고
    • Nonexistence of a steady rarefied supersonic flow in a half-space
    • M. D. Arthur and C. Cercignani, Nonexistence of a steady rarefied supersonic flow in a half-space, Z. Angew. Math. Phys. 31:634-645 (1980).
    • (1980) Z. Angew. Math. Phys. , vol.31 , pp. 634-645
    • Arthur, M.D.1    Cercignani, C.2
  • 7
    • 84990576599 scopus 로고
    • The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas
    • C. Bardos, E. Caflish, and B. Nicolaenko, The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas, Comm. Pure Appl. Math. 39:323-352 (1986).
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 323-352
    • Bardos, C.1    Caflish, E.2    Nicolaenko, B.3
  • 8
    • 0001889361 scopus 로고
    • Thermal layer solutions of the Boltzmann equation
    • Birkhäuser, Massachusetts
    • C. Bardos, E. Caflish, and B. Nicolaenko, Thermal layer solutions of the Boltzmann equation, Progr. Phys. 10:235-251 (Birkhäuser, Massachusetts, 1985).
    • (1985) Progr. Phys. , vol.10 , pp. 235-251
    • Bardos, C.1    Caflish, E.2    Nicolaenko, B.3
  • 9
    • 0001076950 scopus 로고
    • Fluid dynamic limits of kinetic equations I
    • C. Bardos, F. Golse, and C. D. Levermore, Fluid dynamic limits of kinetic equations I, J. Stat. Phys. 63:323-344 (1991).
    • (1991) J. Stat. Phys. , vol.63 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 11
    • 0001315807 scopus 로고
    • The classical incompressible Navier Stokes limit of the Boltzmann equation
    • C. Bardos and S. Ukai, The classical incompressible Navier Stokes limit of the Boltzmann equation, Math. Mod. Meth. Appl. Sci. 1:235-257 (1991).
    • (1991) Math. Mod. Meth. Appl. Sci. , vol.1 , pp. 235-257
    • Bardos, C.1    Ukai, S.2
  • 12
    • 0030496673 scopus 로고    scopus 로고
    • Two-dimensional half space problems for the Broadwell discrete velocity model
    • A. V. Bobylev and G. Toscani, Two-dimensional half space problems for the Broadwell discrete velocity model, Cont. Mech. Thermodyn. 8:257-274 (1996).
    • (1996) Cont. Mech. Thermodyn. , vol.8 , pp. 257-274
    • Bobylev, A.V.1    Toscani, G.2
  • 13
    • 0032342420 scopus 로고    scopus 로고
    • On shock wave solutions for discrete velocity models of the Boltzmann equation
    • C. Bose, R. Illner, and S. Ukai, On shock wave solutions for discrete velocity models of the Boltzmann equation, Transp. Th. Stat. Phys. 27:35-66 (1998).
    • (1998) Transp. Th. Stat. Phys. , vol.27 , pp. 35-66
    • Bose, C.1    Illner, R.2    Ukai, S.3
  • 16
    • 0001615660 scopus 로고
    • On nonlinear stationary half-space problems in discrete kinetic theory
    • C. Cercignani, R. Illner, M. Pulvirenti, and M. Shinbrot, On nonlinear stationary half-space problems in discrete kinetic theory, J. Stat. Phys. 52:885-896 (1988).
    • (1988) J. Stat. Phys. , vol.52 , pp. 885-896
    • Cercignani, C.1    Illner, R.2    Pulvirenti, M.3    Shinbrot, M.4
  • 17
    • 84990563920 scopus 로고
    • Classification of kinetic layer problems
    • F. Coron, F. Golse, and C. Sulem, Classification of kinetic layer problems, Comm. Pure Appl. Math. 41:409-435 (1988).
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 409-435
    • Coron, F.1    Golse, F.2    Sulem, C.3
  • 18
    • 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. 42:1189-1214 (1989).
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 1189-1214
    • De Masi, A.1    Esposito, R.2    Lebowitz, J.L.3
  • 19
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • R. J. DiPerna and P. L. Lions, On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Ann. Math. 130:321-366 (1989).
    • (1989) Ann. Math. , vol.130 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.L.2
  • 20
    • 21344488483 scopus 로고
    • Hydrodynamic limits of the stationary Boltzmann equation in a slab
    • R. Esposito, J. L. Lebowitz, and R. Marra, Hydrodynamic limits of the stationary Boltzmann equation in a slab, Comm. Math. Phys. 160:49-80 (1994).
    • (1994) Comm. Math. Phys. , vol.160 , pp. 49-80
    • Esposito, R.1    Lebowitz, J.L.2    Marra, R.3
  • 21
    • 84988147924 scopus 로고
    • Stationary solutions of the linearized Boltzmann equation in a half space
    • F. Golse and F. Poupaud, Stationary solutions of the linearized Boltzmann equation in a half space, Math. Meth. Appl. Sci. 11:483-502 (1989).
    • (1989) Math. Meth. Appl. Sci. , vol.11 , pp. 483-502
    • Golse, F.1    Poupaud, F.2
  • 22
    • 0001692710 scopus 로고
    • On a boundary layer problem for the nonlinear Boltzmann equation
    • F. Golse, B. Perthame, and C. Sulem, On a boundary layer problem for the nonlinear Boltzmann equation, Arch. Rat. Mech. Anal. 103:81-96 (1988).
    • (1988) Arch. Rat. Mech. Anal. , vol.103 , pp. 81-96
    • Golse, F.1    Perthame, B.2    Sulem, C.3
  • 23
    • 0001351025 scopus 로고
    • Asymptotic theory of the Boltzmann equation
    • H. Grad, Asymptotic theory of the Boltzmann equation, Phys. Fluids 6:147-181 (1963).
    • (1963) Phys. Fluids , vol.6 , pp. 147-181
    • Grad, H.1
  • 24
    • 0001812956 scopus 로고
    • Equation de Boltzmann linéaire dans un demi-éspace
    • J. P. Guiraud, Equation de Boltzmann linéaire dans un demi-éspace, C.R. Acad. Sci. Paris 274:417-419 (1974).
    • (1974) C.r. Acad. Sci. Paris , vol.274 , pp. 417-419
    • Guiraud, J.P.1
  • 25
    • 0034171425 scopus 로고    scopus 로고
    • On a cauchy inequality for the Boltzmann equation
    • A. Nouri, On a Cauchy inequality for the Boltzmann equation, Math. Meth. Appl. Sci. 23:561-573 (2000).
    • (2000) Math. Meth. Appl. Sci. , vol.23 , pp. 561-573
    • Nouri, A.1
  • 27
    • 0000647537 scopus 로고
    • Kinetic theory of evaporation and condensation - Linear and nonlinear problems
    • Y. Sone, Kinetic theory of evaporation and condensation - Linear and nonlinear problems, J. Phys. Soc. Jap. 45:315-320 (1978).
    • (1978) J. Phys. Soc. Jap. , vol.45 , pp. 315-320
    • Sone, Y.1
  • 28
    • 0034386082 scopus 로고    scopus 로고
    • Kinetic theoretical studies of the half-space problem of evaporation and condensation
    • to appear
    • Y. Sone, Kinetic theoretical studies of the half-space problem of evaporation and condensation, Transp. Th. Stat. Phys. (2000), to appear.
    • (2000) Transp. Th. Stat. Phys.
    • Sone, Y.1
  • 29
    • 0001075743 scopus 로고
    • Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hardsphere molecules
    • Y. Sone, T. Ohwada, and K. Aoki, Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hardsphere molecules, Phys. Fluids A 1:1395-1405 (1989).
    • (1989) Phys. Fluids A , vol.1 , pp. 1395-1405
    • Sone, Y.1    Ohwada, T.2    Aoki, K.3
  • 30
    • 0005927309 scopus 로고
    • Evaporation and condensation of a rarefied gas between its two parallel condensed phases with different temperature
    • Springer-Verlag, Berlin
    • Y. Sone, T. Ohwada, and K. Aoki, Evaporation and condensation of a rarefied gas between its two parallel condensed phases with different temperature, Math. aspects of fluid plasma dynamics Proceedings, Lecture Notes in Math, 1460 (Springer-Verlag, Berlin, 1991), pp. 186-202.
    • (1991) Math. Aspects of Fluid Plasma Dynamics Proceedings, Lecture Notes in Math , vol.1460 , pp. 186-202
    • Sone, Y.1    Ohwada, T.2    Aoki, K.3
  • 31
    • 0000908084 scopus 로고    scopus 로고
    • On the half-space problem for the discrete velocity model of the Boltzmann equation
    • World Scientific, Singapore
    • S. Ukai, On the half-space problem for the discrete velocity model of the Boltzmann equation, Advances in Nonlinear PDEs and Stochastics (World Scientific, Singapore, 1998), pp. 160-174.
    • (1998) Advances in Nonlinear PDEs and Stochastics , pp. 160-174
    • Ukai, S.1
  • 32
    • 0001614518 scopus 로고
    • On an entropy dissipation inequality for the Boltzmann equation
    • B. Wennberg, On an entropy dissipation inequality for the Boltzmann equation, C.R. Acad. Sci. Paris 315:1441-1446 (1992).
    • (1992) C.r. Acad. Sci. Paris , vol.315 , pp. 1441-1446
    • Wennberg, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.