Hydrodynamic limits with shock waves of the Boltzmann equation

Communications on Pure and Applied Mathematics

Volumn 58, Issue 3, 2005, Pages 409-443

  Yu, Shih Hsien ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13844256993     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.20027     Document Type: Article

References (15)

1. Boltzmann, L. Lectures on gas theory. Dover, New York, 1964.
2. Caflisch, R. E. The fluid dynamic limit of the nonlinear Boltzmann equation. Comm. Pure Appl. Math. 33 (1980), no. 5, 651-666.
3. Caflisch, R. E.; Nicolaenko, B. Shock profile solutions of the Boltzmann equation. Comm. Math. Phys. 86 (1982), no. 2, 161-194.
4. Cercignani, C.; Illner, R.; Pulvirenti, M. The mathematical theory of dilute gases. Applied Mathematical Sciences, 106. Springer, New York, 1994.
5. Courant, R.; Friedrichs, K. O. Supersonic flow and shock waves. Reprinting of the 1948 original. Applied Mathematical Sciences, 21, Springer, New York-Heidelberg, 1976.
6. Esposito, R.; Pulvirenti, M. From particles to fluid. Handbook of mathematical fluid dynamics, vol. 3. S. Friedlander and D. Serre, eds. North-Holland, Amsterdam, 2004.
7. Goodman, J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rational Mech. Anal. 95 (1986), no. 4, 325-344.
8. Kawashima, S. Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications. Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), no. 1-2, 169-194.
9. Lax, P. D. Hyperbolic systems of conservation laws. II. Comm. Pure Appl. Math. 10 (1957), 537-566.
10. Liu, T.-P. Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 56 (1985), no. 328.
11. Liu, T.-P; Yang, T.; Yu, S.-H. Boltzmann equation: Micro-macro decompositions. Phys. D 188 (2004), 178-192.
12. Liu, T.-P.; Yu, S.-H. Boltzmann equation: Micro-macro decompositions and positivity of shock profiles. Comm. Math. Phys. 246 (2004), 133-179.
13. Nishida, T. Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation. Comm. Math. Phys. 61 (1978), no. 2, 119-148.
14. Sone, Y. Kinetic theory and fluid dynamics. Modeling and Simulation in Science, Engineering, and Technology. Birkhäuser, Boston, 2002.
15. Ukai, S. Les solutions globales de l'èquation de Boltzmann dans l'espace tout entier et dans le demi-espace. C. R. Acad. Sci. Paris Sèr. A-B 282 (1976), no. 6, Ai, A317-A320.