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Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators
One-dimensional compressible Navier-Stokes equations with large density oscillation
1. | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China, China |
References:
[1] |
R. Duan, H.-X. Liu and H.-J. Zhao, Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation, Trans. Amer. Math. Soc., 361 (2009), 453-493.
doi: 10.1090/S0002-9947-08-04637-0. |
[2] |
J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal., 95 (1986), 325-344.
doi: 10.1007/BF00276840. |
[3] |
F.-M. Huang and A. Matsumura, Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation, Comm. Math. Phys., 289 (2009), 841-861.
doi: 10.1007/s00220-009-0843-z. |
[4] |
Ja. Kanel', A model system of equations for the one-dimensional motion of a gas, (Russian) Differencial'nye Uravnenija, 4 (1968), 721-734; English translation in Diff. Eqns., 4 (1968), 374-380. |
[5] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[6] |
T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Amer. Math. Soc., 56 (1985), v+108 pp. |
[7] |
T.-P. Liu, Shock waves for compressible Navier-Stokes equations are stable, Comm. Pure Appl. Math., 39 (1986), 565-594.
doi: 10.1002/cpa.3160390502. |
[8] |
T.-P. Liu and Y.-N. Zeng, On Green's function for hyperbolic-parabolic systems, Acta Math. Sci. Ser. B Engl. Ed., 29 (2009), 1556-1572.
doi: 10.1016/S0252-9602(10)60003-3. |
[9] |
A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, Methods Appl. Anal., 8 (2001), 645-666. |
[10] |
A. Matsumura and M. Mei, Convergence to travelling fronts of solutions of the $p$-system with viscosity in the presence of a boundary, Arch. Ration. Mech. Anal., 146 (1999), 1-22.
doi: 10.1007/s002050050134. |
[11] |
A. Matsumura and K. Nishihara, On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 2 (1985), 17-25.
doi: 10.1007/BF03167036. |
[12] |
A. Matsumura and K. Nishihara, Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 3 (1986), 1-13.
doi: 10.1007/BF03167088. |
[13] |
A. Matsumura and K. Nishihara, Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas, Comm. Math. Phys., 144 (1992), 325-335.
doi: 10.1007/BF02101095. |
[14] |
A. Matsumura and K. Nishihara, Global asymptotics toward the rarefaction wave for solutions of viscous $p$-system with boundary effect, Quart. Appl. Math., 58 (2000), 69-83. |
[15] |
A. Matsumura and K. Nishihara, "Global Solutions for Nonlinear Differential Equations-Mathematical Analysis on Compressible Viscous Fluids," (Japanese), Nippon Hyoronsha, 2004. |
[16] |
K. Nishihara, T. Yang and H.-J. Zhao, Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equations, SIAM J. Math. Anal., 35 (2004), 1561-1597.
doi: 10.1137/S003614100342735X. |
[17] |
J. Smoller, "Shock Waves and Reaction-Diffusion Equations," $2^{nd}$ edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 258, Springer-Verlag, New York, 1994. |
[18] |
K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier-Stokes equations, With an appendix by Helge Kristian Jenssen and Gregory Lyng, in "Handbook of Mathematical Fluid Dynamics," Vol. III, North-Holland, Amsterdam, (2004), 311-533. |
show all references
References:
[1] |
R. Duan, H.-X. Liu and H.-J. Zhao, Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation, Trans. Amer. Math. Soc., 361 (2009), 453-493.
doi: 10.1090/S0002-9947-08-04637-0. |
[2] |
J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal., 95 (1986), 325-344.
doi: 10.1007/BF00276840. |
[3] |
F.-M. Huang and A. Matsumura, Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation, Comm. Math. Phys., 289 (2009), 841-861.
doi: 10.1007/s00220-009-0843-z. |
[4] |
Ja. Kanel', A model system of equations for the one-dimensional motion of a gas, (Russian) Differencial'nye Uravnenija, 4 (1968), 721-734; English translation in Diff. Eqns., 4 (1968), 374-380. |
[5] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[6] |
T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Amer. Math. Soc., 56 (1985), v+108 pp. |
[7] |
T.-P. Liu, Shock waves for compressible Navier-Stokes equations are stable, Comm. Pure Appl. Math., 39 (1986), 565-594.
doi: 10.1002/cpa.3160390502. |
[8] |
T.-P. Liu and Y.-N. Zeng, On Green's function for hyperbolic-parabolic systems, Acta Math. Sci. Ser. B Engl. Ed., 29 (2009), 1556-1572.
doi: 10.1016/S0252-9602(10)60003-3. |
[9] |
A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, Methods Appl. Anal., 8 (2001), 645-666. |
[10] |
A. Matsumura and M. Mei, Convergence to travelling fronts of solutions of the $p$-system with viscosity in the presence of a boundary, Arch. Ration. Mech. Anal., 146 (1999), 1-22.
doi: 10.1007/s002050050134. |
[11] |
A. Matsumura and K. Nishihara, On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 2 (1985), 17-25.
doi: 10.1007/BF03167036. |
[12] |
A. Matsumura and K. Nishihara, Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 3 (1986), 1-13.
doi: 10.1007/BF03167088. |
[13] |
A. Matsumura and K. Nishihara, Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas, Comm. Math. Phys., 144 (1992), 325-335.
doi: 10.1007/BF02101095. |
[14] |
A. Matsumura and K. Nishihara, Global asymptotics toward the rarefaction wave for solutions of viscous $p$-system with boundary effect, Quart. Appl. Math., 58 (2000), 69-83. |
[15] |
A. Matsumura and K. Nishihara, "Global Solutions for Nonlinear Differential Equations-Mathematical Analysis on Compressible Viscous Fluids," (Japanese), Nippon Hyoronsha, 2004. |
[16] |
K. Nishihara, T. Yang and H.-J. Zhao, Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equations, SIAM J. Math. Anal., 35 (2004), 1561-1597.
doi: 10.1137/S003614100342735X. |
[17] |
J. Smoller, "Shock Waves and Reaction-Diffusion Equations," $2^{nd}$ edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 258, Springer-Verlag, New York, 1994. |
[18] |
K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier-Stokes equations, With an appendix by Helge Kristian Jenssen and Gregory Lyng, in "Handbook of Mathematical Fluid Dynamics," Vol. III, North-Holland, Amsterdam, (2004), 311-533. |
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