Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum

Communications in Mathematical Physics

Volumn 230, Issue 2, 2002, Pages 329-363

  Yang, Tong ^a,b   Zhu, Changjiang ^a,b  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036027002     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0703-6     Document Type: Article

References (25)

1. Balian, R.: From microphysics to macrophysics. Texts and Monographs in Physics. Berlin-Heidelberg-New York: Springer, 1982
2. Chen, G.Q., Hoff, D., Trivisa, K.: Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data. Comm. Partial Differential Equations 25, 2233-2257 (2000)
3. Chen, G.Q., Kratka, M.: Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary. Preprint 2000
4. Grad, H.: Asymptotic theory of the Boltzmann equation II. In: Rarefied Gas Dynamics, 1. J. Laurmann, ed., New York: Academic Press, 1963, pp. 26-59
5. Hoff, D.: Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data. Arch. Rat. Mech. Anal. 132, 1-14 (1995)
6. Hoff, D., Liu, T.-P.: The inviscid limit for the Navier-Stokes equations of compressible isentropic flow with shock data. Indiana Univ. Math. J. 38, 861-915 (1989)
7. Hoff, D., Serre, D.: The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow. SIAM J. Appl. Math. 51, 887-898 (1991)
8. Hoff, D., Smoller, J.: Non-formation of vacuum states for compressible Navier-Stokes equations. Commun. Math. Phys. 216, 255-276 (2001)
9. Jiang, S.: Global smooth solutions of the equations of a viscous, heat-conducting, one-dimensional gas with density-dependent viscosity. Math. Nachr. 190, 169-183 (1998)
10. Jiang, S., Xin, Z.P., Zhang, P.: Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity. Preprint 1999
11. Kawashima, S., Nishida, T.: The initial-value problems for the equations of viscous compressible and perfect compressible fluids. In: RIMS, Kokyuroku 428, Kyoto University, Nonlinear Functional Analysis, June 1981, pp. 34-59
12. Lions, P.L.: Mathematical Topics in Fluid Mechanics. Vols. 1, 2, 1998, Oxford: Clarendon Press, 1998
13. Liu, T.-P., Xin, Z., Yang, T.: Vacuum states of compressible flow. Discrete and Continuous Dynamical Systems 4, 1-32 (1998)
14. Luo, T., Xin, Z., Yang, T.: Interface behavior of compressible Navier-Stokes equations with vacuum. SIAM J. Math. Anal. 31, 1175-1191 (2000)
15. Makino, T.: On a local existence theorem for the evolution equations of gaseous stars. In: Patterns and Wave-qualitative Analysis of Nonlinear Differential Equations. T. Nishida, M. Mimura, H. Fujii, ed., Amsterdam: North-Holland, 1986, pp. 459-479
16. Nishida, T.: Equations of fluid dynamics-free surface problems. Comm. Pure Appl. Math. XXXIX, 221-238 (1986)
17. Nishida, T.: Equations of motion of compressible viscous fluids. In: Patterns and Waves - Qualitative Analysis of Nonlinear Differential Equations, 1986, pp. 97-128
18. Okada, M.: Free boundary value problems for the equation of one-dimensional motion of viscous gas. Japan J. Appl. Math. 6, 161-177 (1989)
19. Okada, M., Makino, T.: Free boundary problem for the equations of spherically symmetrical motion of viscous gas. Japan J. Indust. Appl. Math. 10, 219-235 (1993)
20. Okada, M., Matušu̇-Nečasová, Š., Makino, T.: Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity. Preprint, 1999
21. Serre, D.: Sur l'Equation mondimensionnelle d'Un fluide visqueux, compressible et conducteur de chaleur. Comptes rendus Acad. des Sciences 303, 703-706 (1986)
22. Xin, Z.: Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Comm. Pure Appl. Math. 51, 229-240 (1998)
23. Yang, T.: Some recent results on compressible flow with vacuum. Taiwanese J. Math. 4, 33-44 (2000)
24. Yang, T., Yao, Z.A., Zhu, C.J.: Compressible Navier-Stokes equations with density-dependent viscosity and vacuum. Comm. Partial Differential Eqs. 26, 965-981 (2001)
25. Yang, T., Zhao, H.J.: A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Preprint, 2001