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Volumn 190, Issue 1-2, 2006, Pages 211-231

Singular behavior of vacuum states for compressible fluids

Author keywords

Boltzmann equation; Euler equations; Euler Poisson equations; Navier Stokes equations; Vacuum singularity

Indexed keywords

FLUIDS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; VACUUM;

EID: 32044470937     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.01.043     Document Type: Conference Paper
Times cited : (44)

References (76)
  • 1
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and application
    • A. Ambrosetti, and P. Rabinowitz Dual variational methods in critical point theory and application J. Funct. Anal. 14 1973 349 381
    • (1973) J. Funct. Anal. , vol.14 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.2
  • 2
    • 0040430170 scopus 로고
    • How an initial stationary interface begins to move in porous media flow
    • D.G. Aronson, L.A. Caffarelli, and S. Kamin How an initial stationary interface begins to move in porous media flow SIAM J. Math. Anal. 14 1983 639 658
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 639-658
    • Aronson, D.G.1    Caffarelli, L.A.2    Kamin, S.3
  • 3
    • 0001076950 scopus 로고
    • Fluid dynamic limits of kinetic equations, I. Formal derivations
    • C. Bardos, F. Glose, and D. Levermore Fluid dynamic limits of kinetic equations, I. Formal derivations Comm. Pure Appl. Math. 63 1991 323 344
    • (1991) Comm. Pure Appl. Math. , vol.63 , pp. 323-344
    • Bardos, C.1    Glose, F.2    Levermore, D.3
  • 4
    • 84990619144 scopus 로고
    • Levermore Fluid dynamic limits of kinetic equations, II. Convergence proofs for the Boltzmann equation
    • 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
  • 5
    • 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. Models Methods Appl. Sci. 1 2 1991 235 257
    • (1991) Math. Models Methods Appl. Sci. , vol.1 , Issue.2 , pp. 235-257
    • Bardos, C.1    Ukai, S.2
  • 6
    • 0001523009 scopus 로고
    • Existence locale pour les équations d'Euler-Poisson
    • M. Béard Existence locale pour les équations d'Euler-Poisson Japan J. Indust. Appl. Math. 10 1993 431 450
    • (1993) Japan J. Indust. Appl. Math. , vol.10 , pp. 431-450
    • Béard, M.1
  • 8
    • 0000229982 scopus 로고
    • Weitere studien uber das Warme gleichgenicht unfer Gasmolekular. Sitzungsberichte der Akademie der Wissenschaften
    • L. Boltzmann Weitere studien uber das Warme gleichgenicht unfer Gasmolekular. Sitzungsberichte der Akademie der Wissenschaften Wien 66 1872 275 370
    • (1872) Wien , vol.66 , pp. 275-370
    • Boltzmann, L.1
  • 9
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
    • J.-M. Bony Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires Annales de l'École Normale Supérieure 14 1981 209 246
    • (1981) Annales de l'École Normale Supérieure , vol.14 , pp. 209-246
    • Bony, J.-M.1
  • 10
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic involving critical Sobolev exponents
    • H. Brezis, and L. Nirenberg Positive solutions of nonlinear elliptic involving critical Sobolev exponents Comm. Pure Appl. Math. 36 1983 437 477
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 13
    • 0003312241 scopus 로고
    • Fluides parfaits incompressibles
    • J.-Y. Chemin Fluides parfaits incompressibles Astérisque 230 1995
    • (1995) Astérisque , vol.230
    • Chemin, J.-Y.1
  • 14
    • 0036383333 scopus 로고    scopus 로고
    • Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary
    • G.Q. Chen, and M. Kratka Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary Comm. Partial Differential Equations 27 5-6 2002 907 943
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.5-6 , pp. 907-943
    • Chen, G.Q.1    Kratka, M.2
  • 16
    • 0142024001 scopus 로고    scopus 로고
    • Blowup phenomena of the Euler-Poisson equations for gaseous stars
    • Y.B. Deng, J.L. Xiang, and T. Yang Blowup phenomena of the Euler-Poisson equations for gaseous stars J. Math. Anal. Appl. 286 2003 295 306
    • (2003) J. Math. Anal. Appl. , vol.286 , pp. 295-306
    • Deng, Y.B.1    Xiang, J.L.2    Yang, T.3
  • 18
    • 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. of Math. 130 1989 321 366
    • (1989) Ann. of Math. , vol.130 , pp. 321-366
    • Diperna, R.J.1    Lions, P.L.2
  • 19
    • 0001094592 scopus 로고
    • Solution reguliere a temps petit pour l'equation d'Euler-Poisson
    • P. Gamblin Solution reguliere a temps petit pour l'equation d'Euler-Poisson Comm. Partial Differential Equations 18 1993 731 745
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 731-745
    • Gamblin, P.1
  • 20
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • B. Gidas, W.M. Ni, and L. Nirenberg Symmetry and related properties via the maximum principle Comm. Math. Phys. 68 1979 209 243
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 22
    • 0003138434 scopus 로고
    • Asymptotic theory of the Boltzmann equation II
    • J. Laurmann Academic Press New York
    • H. Grad Asymptotic theory of the Boltzmann equation II J. Laurmann Rarefied Gas Dynamics 1963 Academic Press New York 26 59
    • (1963) Rarefied Gas Dynamics , pp. 26-59
    • Grad, H.1
  • 23
    • 0038478202 scopus 로고    scopus 로고
    • Global smooth solutions to Euler equations for an isentropic perfect gas
    • M. Grassin, and D. Serre Global smooth solutions to Euler equations for an isentropic perfect gas C.R. Acad. Sci. Paris Sér. I Math 325 7 1997 721 726
    • (1997) C.R. Acad. Sci. Paris Sér. i Math , vol.325 , Issue.7 , pp. 721-726
    • Grassin, M.1    Serre, D.2
  • 24
    • 0035531905 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system bear vacuum
    • Y. Guo The Vlasov-Poisson-Boltzmann system bear vacuum Comm. Math. Phys. 218 2 2001 293 313
    • (2001) Comm. Math. Phys. , vol.218 , Issue.2 , pp. 293-313
    • Guo, Y.1
  • 25
    • 21844497460 scopus 로고
    • Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data
    • D. Hoff Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data Arch. Rational Mech. Anal. 132 1995 1 14
    • (1995) Arch. Rational Mech. Anal. , vol.132 , pp. 1-14
    • Hoff, D.1
  • 26
    • 0026207013 scopus 로고
    • The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow
    • D. Hoff, and D. Serre The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow SIAM J. Appl. Math. 51 1991 887 898
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 887-898
    • Hoff, D.1    Serre, D.2
  • 27
    • 0035529616 scopus 로고    scopus 로고
    • Non-formation of vacuum states for compressible Navier-Stokes equations
    • D. Hoff, and J. Smoller Non-formation of vacuum states for compressible Navier-Stokes equations Comm. Math. Phys. 216 2001 255 276
    • (2001) Comm. Math. Phys. , vol.216 , pp. 255-276
    • Hoff, D.1    Smoller, J.2
  • 29
    • 0000580833 scopus 로고
    • Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
    • L. Hsiao, and T.-P. Liu Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping Comm. Math. Phys. 143 1992 599 605
    • (1992) Comm. Math. Phys. , vol.143 , pp. 599-605
    • Hsiao, L.1    Liu, T.-P.2
  • 30
    • 0037934303 scopus 로고    scopus 로고
    • Convergence rate for compressible Euler equations with damping and vacuum
    • F.M. Huang, and R.H. Pan Convergence rate for compressible Euler equations with damping and vacuum Arch. Rational Mech. Anal. 16 4 2003 359 376
    • (2003) Arch. Rational Mech. Anal. , vol.16 , Issue.4 , pp. 359-376
    • Huang, F.M.1    Pan, R.H.2
  • 31
    • 0001467016 scopus 로고
    • Global validity of the Boltzmann equation for two- and three-dimensional rare gases in vacuum
    • R. Illner, and M. Pulvirenti Global validity of the Boltzmann equation for two- and three-dimensional rare gases in vacuum Comm. Math. Phys. 105 1986 189 203
    • (1986) Comm. Math. Phys. , vol.105 , pp. 189-203
    • Illner, R.1    Pulvirenti, M.2
  • 32
    • 34250139505 scopus 로고
    • The Boltzmann equation: Global existence for a rare gas in an infinite vacuum
    • R. Illner, and M. Shinbrot The Boltzmann equation: Global existence for a rare gas in an infinite vacuum Comm. Math. Phys. 95 1984 217 226
    • (1984) Comm. Math. Phys. , vol.95 , pp. 217-226
    • Illner, R.1    Shinbrot, M.2
  • 34
    • 0040943239 scopus 로고
    • The Boltzmann equation. I. Uniqueness and local existence
    • S. Kaniel, and M. Shinbrot The Boltzmann equation. I. Uniqueness and local existence Comm. Math. Phys. 59 1978 65 84
    • (1978) Comm. Math. Phys. , vol.59 , pp. 65-84
    • Kaniel, S.1    Shinbrot, M.2
  • 35
    • 0016594542 scopus 로고
    • The Cauchy problem for quasi-linear symmetric hyperbolic systems
    • T. Kato The Cauchy problem for quasi-linear symmetric hyperbolic systems Arch. Rational Mech. Anal. 58 1945 181 205
    • (1945) Arch. Rational Mech. Anal. , vol.58 , pp. 181-205
    • Kato, T.1
  • 36
    • 0040193736 scopus 로고
    • On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
    • S. Kawashima, A. Matsumura, and T. Nishida On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation Comm. Math. Phys. 70 2 1979 97 124
    • (1979) Comm. Math. Phys. , vol.70 , Issue.2 , pp. 97-124
    • Kawashima, S.1    Matsumura, A.2    Nishida, T.3
  • 37
    • 84968487166 scopus 로고
    • The porous medium equation in one dimension
    • B. Knerr The porous medium equation in one dimension Trans. Amer. Math. Soc. 234 2 1977
    • (1977) Trans. Amer. Math. Soc. , vol.234 , Issue.2
    • Knerr, B.1
  • 38
    • 0000542025 scopus 로고
    • Variable stars
    • Springer, Berlin
    • P. Ledowx, T. Welrevein, Variable stars, Handbuch der Physic, Bd. LI (1958), Springer, Berlin, pp. 353-604.
    • (1958) Handbuch der Physic , vol.51 , pp. 353-604
    • Ledowx, P.1    Welrevein, T.2
  • 39
    • 0031513495 scopus 로고    scopus 로고
    • Stability of gaseous stars in spherically symmetric motions
    • S.S. Lin Stability of gaseous stars in spherically symmetric motions SIAM J. Math. Anal. 28 3 1997 539 569
    • (1997) SIAM J. Math. Anal. , vol.28 , Issue.3 , pp. 539-569
    • Lin, S.S.1
  • 40
    • 0023291684 scopus 로고
    • On the vacuum state for the equations of isentropic gas dynamics
    • L.W. Lin On the vacuum state for the equations of isentropic gas dynamics J. Math. Anal. Appl. 121 2 1987 406 425
    • (1987) J. Math. Anal. Appl. , vol.121 , Issue.2 , pp. 406-425
    • Lin, L.W.1
  • 43
    • 0035616508 scopus 로고    scopus 로고
    • From the Boltzmann to the equations of incompressible fluid mechanics, i
    • P.-L. Lions, and N. Masmoudi From the Boltzmann to the equations of incompressible fluid mechanics, I 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
  • 44
    • 0002680118 scopus 로고    scopus 로고
    • Compressible flow with damping and vacuum
    • T.-P. Liu Compressible flow with damping and vacuum Japan J. Appl. Math. 13 1 1996 25 32
    • (1996) Japan J. Appl. Math. , vol.13 , Issue.1 , pp. 25-32
    • Liu, T.-P.1
  • 45
    • 0000710622 scopus 로고
    • On the vacuum state for isentropic gas dynamics equations
    • T.-P. Liu, and J. Smoller On the vacuum state for isentropic gas dynamics equations Adv. in Math. 1 1980 345 359
    • (1980) Adv. in Math. , vol.1 , pp. 345-359
    • Liu, T.-P.1    Smoller, J.2
  • 47
    • 0001736387 scopus 로고    scopus 로고
    • Compressible Euler equations with vacuum
    • T.-P. Liu, and T. Yang Compressible Euler equations with vacuum J. Differential Equations 140 2 1997 223 237
    • (1997) J. Differential Equations , vol.140 , Issue.2 , pp. 223-237
    • Liu, T.-P.1    Yang, T.2
  • 48
    • 0012944154 scopus 로고    scopus 로고
    • Compressible flow with vacuum and physical singularity
    • T.-P. Liu, and T. Yang Compressible flow with vacuum and physical singularity Methods Appl. Anal. 7 3 2000 495 510
    • (2000) Methods Appl. Anal. , vol.7 , Issue.3 , pp. 495-510
    • Liu, T.-P.1    Yang, T.2
  • 49
    • 0346498040 scopus 로고    scopus 로고
    • Energy method for Boltzmann equation
    • T.-P. Liu, T. Yang, and S.-H. Yu Energy method for Boltzmann equation Physica D 188 2004 178 192
    • (2004) Physica D , vol.188 , pp. 178-192
    • Liu, T.-P.1    Yang, T.2    Yu, S.-H.3
  • 50
    • 6344265887 scopus 로고    scopus 로고
    • Rotating fluids with self-gravitation in bounded domains
    • T. Luo, J. Smoller, Rotating fluids with self-gravitation in bounded domains, Arch. Rational Mech. Anal. (2004).
    • (2004) Arch. Rational Mech. Anal.
    • Luo, T.1    Smoller, J.2
  • 51
    • 0034178643 scopus 로고    scopus 로고
    • Interface behavior of compressible Navier-Stokes equations with vacuum
    • T. Luo, Z. Xin, and T. Yang Interface behavior of compressible Navier-Stokes equations with vacuum SIAM J. Math. Anal. 31 2000 1175 1191
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 1175-1191
    • Luo, T.1    Xin, Z.2    Yang, T.3
  • 52
    • 84963385957 scopus 로고
    • Blowing up solutions of the Euler-Poisson equation for the evolution of gaseous stars
    • T. Makino Blowing up solutions of the Euler-Poisson equation for the evolution of gaseous stars Transport Theory Statist. Phys. 21 1992 615 624
    • (1992) Transport Theory Statist. Phys. , vol.21 , pp. 615-624
    • Makino, T.1
  • 53
    • 77957028939 scopus 로고
    • On a local existence theorem for the evolution equations of gaseous stars
    • T. Nishida M. Mimura H. Fujii North-Holland Amsterdam
    • T. Makino On a local existence theorem for the evolution equations of gaseous stars T. Nishida M. Mimura H. Fujii Patterns and Wave-qualitative Analysis of Nonlinear Differential Equations 1986 North-Holland Amsterdam 459 479
    • (1986) Patterns and Wave-qualitative Analysis of Nonlinear Differential Equations , pp. 459-479
    • Makino, T.1
  • 54
    • 0001257150 scopus 로고
    • Sur les Solutions a symmetric spherique de lequation d'Euler-Poisson Pour levolution d'etoiles gazeuses
    • T. Makino, and B. Perthame Sur les Solutions a symmetric spherique de lequation d'Euler-Poisson Pour levolution d'etoiles gazeuses Japan J. Appl. Math. 7 1990 165 170
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 165-170
    • Makino, T.1    Perthame, B.2
  • 55
    • 0000653982 scopus 로고
    • Sur l'existence des solutions locales de léquation d'Euler-Poisson pour l'evolution gazeuses
    • T. Makino, and S. Ukai Sur l'existence des solutions locales de léquation d'Euler-Poisson pour l'evolution gazeuses J. Math. Kyoto Univ. 27 1987 387 399
    • (1987) J. Math. Kyoto Univ. , vol.27 , pp. 387-399
    • Makino, T.1    Ukai, S.2
  • 56
    • 0004022482 scopus 로고
    • Cambridge University Press, Cambridge Reprinted by Dover Publications, New York, 1965
    • J.C. Maxwell, Scientific Papers. vol. 2, Cambridge University Press, Cambridge, 1890 (Reprinted by Dover Publications, New York, 1965).
    • (1890) Scientific Papers , vol.2
    • Maxwell, J.C.1
  • 57
    • 84990576581 scopus 로고
    • Uniqueness and nonuniqueness for positive radial solutions of -Δ = f(u,r)
    • W.M. Ni, and R.D. Nussbaum Uniqueness and nonuniqueness for positive radial solutions of - Δ u = f (u, r ) Comm. Pure Appl. Math. 38 1985 67 108
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 67-108
    • Ni, W.M.1    Nussbaum, R.D.2
  • 58
    • 0011400198 scopus 로고
    • Nonlinear hyperbolic equations and related topics in fluid dynamics
    • T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Publ. Math. (1978) 46-53.
    • (1978) Publ. Math. , pp. 46-53
    • Nishida, T.1
  • 59
    • 32044444972 scopus 로고
    • Asymptotic behavior of solutions of the Boltzmann equation
    • Trends in applications of pure mathematics to mechanics Edinburgh Pitman, Boston, Massachusetts, London
    • T. Nishida, Asymptotic behavior of solutions of the Boltzmann equation. Trends in applications of pure mathematics to mechanics, vol. III, Edinburgh, 1979, pp. 190-203, Monographs Stud. Math., vol. 11, Pitman, Boston, Massachusetts, London, 1981.
    • (1979) Monographs Stud. Math. , vol.3 , pp. 190-203
    • Nishida, T.1
  • 60
    • 0000470158 scopus 로고
    • Free boundary value problems for the equation of one-dimensional motion of viscous gas
    • M. Okada Free boundary value problems for the equation of one-dimensional motion of viscous gas Japan J. Appl. Math. 6 1989 161 177
    • (1989) Japan J. Appl. Math. , vol.6 , pp. 161-177
    • Okada, M.1
  • 61
    • 0000236035 scopus 로고
    • Free boundary problem for the equation of spherically symmetrical motion of viscous gas
    • M. Okada, and T. Makino Free boundary problem for the equation of spherically symmetrical motion of viscous gas Japan J. Indust. Appl. Math. 10 1993 219 235
    • (1993) Japan J. Indust. Appl. Math. , vol.10 , pp. 219-235
    • Okada, M.1    Makino, T.2
  • 62
    • 77249090092 scopus 로고    scopus 로고
    • Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity
    • M. Okada, Š. Matušu̇-Nečasová, and T. Makino Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity Ann. Univ. Ferrara Sez. VII(N.S). 48 2002 1 20
    • (2002) Ann. Univ. Ferrara Sez. VII(N.S). , vol.48 , pp. 1-20
    • Okada, M.1    Matušu-Nečasová, Š.2    Makino, T.3
  • 63
    • 84980167508 scopus 로고
    • On the Cauchy problem for weakly hyperbolic equations
    • O.A. Oleinik On the Cauchy problem for weakly hyperbolic equations Comm. Pure Appl. Math. XXIII 1970 569 586
    • (1970) Comm. Pure Appl. Math. , vol.23 , pp. 569-586
    • Oleinik, O.A.1
  • 64
    • 0001620268 scopus 로고
    • Sur l'equation mondimensionnelle d'un fluide visqueux, compressible et conducteur de chaleur
    • D. Serre Sur l'equation mondimensionnelle d'un fluide visqueux, compressible et conducteur de chaleur Comptes rendus Acad. des Sciences 303 1986 703 706
    • (1986) Comptes Rendus Acad. des Sciences , vol.303 , pp. 703-706
    • Serre, D.1
  • 66
    • 0009328610 scopus 로고    scopus 로고
    • Les solutions globales de l'équation non linéaire de Boltzmann dans l'espace tout entier et dans demi-espace
    • S. Ukai Les solutions globales de l'équation non linéaire de Boltzmann dans l'espace tout entier et dans demi-espace C.R. Acad. Sci. (Paris) A 282 1996 317 320
    • (1996) C.R. Acad. Sci. (Paris) A , vol.282 , pp. 317-320
    • Ukai, S.1
  • 68
    • 0043159149 scopus 로고    scopus 로고
    • Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum (II)
    • S.W. Vong, T. Yang, and C.J. Zhu Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum (II) J. Differential Equations 192 2003 475 501
    • (2003) J. Differential Equations , vol.192 , pp. 475-501
    • Vong, S.W.1    Yang, T.2    Zhu, C.J.3
  • 69
    • 0032358560 scopus 로고    scopus 로고
    • Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density
    • Z. Xin Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density Comm. Pure Appl. Math. 51 1998 229 240
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 229-240
    • Xin, Z.1
  • 70
    • 32044434327 scopus 로고    scopus 로고
    • Local existence with physical vacuum boundary condition to Euler equations with damping
    • C.J. Xu, T. Yang, Local existence with physical vacuum boundary condition to Euler equations with damping, J. Differential Equations (2004).
    • (2004) J. Differential Equations
    • Xu, C.J.1    Yang, T.2
  • 71
    • 0003010327 scopus 로고    scopus 로고
    • Some recent results on compressible flow with vacuum
    • T. Yang Some recent results on compressible flow with vacuum Taiwanese J. Math. 4 2000 33 44
    • (2000) Taiwanese J. Math. , vol.4 , pp. 33-44
    • Yang, T.1
  • 72
    • 0000895412 scopus 로고    scopus 로고
    • Compressible Navier-Stokes with density-dependent viscosity and vacuum
    • T. Yang, Z.A. Yao, and C.J. Zhu Compressible Navier-Stokes with density-dependent viscosity and vacuum Comm. Partial Differential Equations 26 2001 965 981
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 965-981
    • Yang, T.1    Yao, Z.A.2    Zhu, C.J.3
  • 73
    • 0036750329 scopus 로고    scopus 로고
    • A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
    • T. Yang, and H.J. Zhao A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity J. Differential Equations 184 2002 163 184
    • (2002) J. Differential Equations , vol.184 , pp. 163-184
    • Yang, T.1    Zhao, H.J.2
  • 74
    • 0036027002 scopus 로고    scopus 로고
    • Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum
    • T. Yang, and C.J. Zhu Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum Commun. Math. Phys. 230 2002 329 363
    • (2002) Commun. Math. Phys. , vol.230 , pp. 329-363
    • Yang, T.1    Zhu, C.J.2
  • 75
    • 0034148420 scopus 로고    scopus 로고
    • Existence and non-existence of global smooth solutions for p-system with relaxation
    • T. Yang, and C.J. Zhu Existence and non-existence of global smooth solutions for p-system with relaxation J. Differential Equations 161 2000 321 336
    • (2000) J. Differential Equations , vol.161 , pp. 321-336
    • Yang, T.1    Zhu, C.J.2
  • 76
    • 30244572333 scopus 로고    scopus 로고
    • Non-existence of global smooth solutions to symmetrizable nonlinear hyperbolic systems
    • T. Yang, and C.J. Zhu Non-existence of global smooth solutions to symmetrizable nonlinear hyperbolic systems Proc. Roy. Soc. Edinburgh 133A 2003 719 728
    • (2003) Proc. Roy. Soc. Edinburgh , vol.133 , pp. 719-728
    • Yang, T.1    Zhu, C.J.2


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