Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum

Communications on Pure and Applied Mathematics

Volumn 64, Issue 3, 2011, Pages 328-366

  Coutand, Daniel ^a   Shkoller, Steve ^b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650229802     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20344     Document Type: Article

References (18)

1. Coutand, D.; Lindblad, H.; Shkoller, S. A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum. Comm. Math. Phys. 296 (2010), no. 2, 559-587.
2. Coutand, D.; Shkoller, S. The interaction between quasilinear elastodynamics and the Navier-Stokes equations. Arch. Ration. Mech. Anal. 179 (2006), no. 3, 303-352.
3. Coutand, D.; Shkoller, S. Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Amer. Math. Soc. 20 (2007), no. 3, 829-930.
4. Coutand, D.; Shkoller, S. Well-posedness in smooth function spaces for the moving-boundary 3-D compressible Euler equations in physical vacuum. Preprint, 2010. Available at.
5. Deimling, K. Nonlinear functional analysis. Springer, Berlin, 1985.
6. Jang, J.; Masmoudi, N. Well-posedness for compressible Euler equations with physical vacuum singularity. Comm. Pure Appl. Math. 62 (2009), no. 10, 1327-1385.
7. Kufner, A. Weighted Sobolev spaces. Wiley-Interscience, New York, 1985.
8. Lin, L. W. On the vacuum state for the equations of isentropic gas dynamics. J. Math. Anal. Appl. 121 (1987), no. 2, 406-425.
9. Lindblad, H. Well posedness for the motion of a compressible liquid with free surface boundary. Comm. Math. Phys. 260 (2005), no. 2, 319-392.
10. Liu, T.-P. Compressible flow with damping and vacuum. Japan J. Indust. Appl. Math. 13 (1996), no. 1, 25-32.
11. Liu, T.-P.; Smoller, J. A. On the vacuum state for the isentropic gas dynamics equations. Adv. in Appl. Math. 1 (1980), no. 4, 345-359.
12. Liu, T.-P.; Yang, T. Compressible Euler equations with vacuum. J. Differential Equations 140 (1997), no. 2, 223-237.
13. Liu, T.-P.; Yang, T. Compressible flow with vacuum and physical singularity. Methods Appl. Anal. 7 (2000), no. 3, 495-510.
14. Makino, T. On a local existence theorem for the evolution equation of gaseous stars. Patterns and waves, 459-479. Studies in Mathematics and Its Applications, 18. North-Holland, Amsterdam, 1986.
15. Masmoudi, N. Video of Discussion: Free boundary problems related to water waves. Summer Program: Nonlinear Conservation Laws and Applications, July 13-31, 2009, Institute for Mathematics and Its Applications, University of Minnesota. Available at.
16. Trakhinin, Y. Local existence for the free boundary problem for nonrelativistic and relativistic compressible Euler equations with a vacuum boundary condition. Comm. Pure Appl. Math. 62 (2009), no. 11, 1551-1594.
17. Xu, C.-J.; Yang, T. Local existence with physical vacuum boundary condition to Euler equations with damping. J. Differential Equations 210 (2005), no. 1, 217-231.
18. Yang, T. Singular behavior of vacuum states for compressible fluids. J. Comput. Appl. Math. 190 (2006), no. 1-2, 211-231.