Well-posedness for compressible Euler equations with physical vacuum singularity

Communications on Pure and Applied Mathematics

Volumn 62, Issue 10, 2009, Pages 1327-1385

  Jang, Juhi ^a   Masmoudi, Nader ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68049131315     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20285     Document Type: Article

References (26)

1. Alvarez-Samaniego, B.; Lannes, D. Large time existence for 3D water-waves and asymptotics. Invent. Math. 171 (2008), no. 3, 485-541.
2. Ambrose, D. M; Masmoudi, N. The zero surface tension limit of two-dimensional water waves. Comm. Pure Appl. Math. 58 (2005), no. 10, 1287-1315.
3. Ambrose, D. M; Masmoudi, N. Well-posedness of 3D vortex sheets with surface tension, Commun. Math. Sci. 5 (2007), 391-430.
4. Chemin, J.-Y. Dynamique des gaz à masse totale finie. Asymptotic Anal. 3 (1990), 215-220.
5. 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 (electronic).
6. Grassin, M. Global smooth solutions to Euler equations for a perfect gas. Indiana Univ. Math. J. 47 (1998), no. 4, 1397-1432.
7. Huang, F.; Marcati, P.; Pan, R. Convergence to the Barenblatt solution for the compressible Euler equations with damping and vacuum. Arch. Ration. Mech. Anal. 176 (2005), 1-24.
8. Jang, J. Local wellposedness of viscous gaseous stars. Arch. Ration. Mech. Anal., in press.
9. Lindblad, H.Well posedness for the motion of a compressible liquid with free surface boundary. Comm. Math. Phys. 260 (2005), 319-392.
10. Liu, T.-P. Compressible flow with damping and vacuum. Japan J. Appl. Math. 13 (1996), 25-32.
11. Liu, T.-P.; Smoller, J. On the vacuum state for isentropic gas dynamics equations. Advances in Math. 1 (1980), 345-359.
12. Liu, T.-P.; Yang, T. Compressible Euler equations with vacuum. J. Differential Equations 140 (1997), 223-237.
13. Liu, T.-P.; Yang, T. Compressible flow with vacuum and physical singularity. Methods Appl. Anal. 7 (2000), 495-509.
14. Luo, T.; Xin, Z.; Yang, T. Interface behavior of compressible Navier-Stokes equations with vacuum. SIAM J. Math. Anal. 31 (2000), 1175-1191.
15. Majda, A. Compressible fluid flow and systems of conservation laws in several space variables. Applied Mathematical Sciences, 53. Springer, New York, 1984.
16. Makino, T. Blowing up solutions of the Euler-Poisson equation for the evolution of gaseous stars. Proceedings of the Fourth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics (Kyoto, 1991), Transport Theory Statist. Phys., 21 (1992), no. 4-6, 615-624.
17. Makino, T.; Ukai, S. Sur l'existence des solutions locales de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses. J. Math. Kyoto Univ. 27 (1987), 387-399
18. Makino, T.; Ukai, S.; Kawashima, S. Sur la solution à support compact de l'équations d'Euler compressible. Japan J. Appl. Math. 3 (1986), 249-257.
19. Masmoudi, N. Well-posedness for the FENE dumbbell model of polymeric flows. Comm. Pure Appl. Math. 61 (2008), no. 12, 1685-1714.
20. Serre, D. Solutions classiques globales des équations d'Euler pour un fluide parfait compressible. Ann. Inst. Fourier (Grenoble) 47 (1997), 139-153.
21. Shatah, J.; Zeng, C. Geometry and a priori estimates for free boundary problems of the Euler equation. Comm. Pure Appl. Math. 61 (2008), 698-744.
22. Shkoller, S. Personal communication, 2008.
23. Sideris, T. C. Formation of singularities in three-dimensional compressible fluids. Comm. Math. Phys. 101 (1985), 475-485.
24. Xu, C.-J.; Yang, T. Local existence with physical vacuum boundary condition to Euler equations with damping. J. Differential Equations 210 (2005), 217-231.
25. Yang, T. Singular behavior of vacuum states for compressible fluids. Comput. Appl. Math. 190 (2006), 211-231.
26. Zhang, P.; Zhang, Z. On the free boundary problem of three-dimensional incompressible Euler equations. Comm. Pure Appl. Math. 61 (2008), no. 7, 877-940.