Transactions of the American Mathematical Society

Author(s): Jean-François Coulombel; Thierry Goudon
Journal: Trans. Amer. Math. Soc. 359 (2007), 637-648.
MSC (2000): Primary 35L25; Secondary 35L65, 35L45, 76N15
Posted: July 21, 2006
Retrieve article in: PDF DVI PostScript

Abstract: We construct global smooth solutions to the multidimensional isothermal Euler equations with a strong relaxation. When the relaxation time tends to zero, we show that the density converges towards the solution to the heat equation.

1.: S. Alinhac, P. Gérard, Opérateurs pseudo-différentiels et théorème de Nash-Moser, InterEditions, 1991. MR 1172111 (93g:35001)
2.: B. Hanouzet, R. Natalini, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal. 169 (2003), no. 2, 89-117. MR 2005637 (2004h:35135)
3.: S. Junca, M. Rascle, Strong relaxation of the isothermal Euler system to the heat equation, Z. Angew. Math. Phys. 53 (2002), no. 2, 239-264.MR 1900673 (2003d:35215)
4.: T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal. 58 (1975), no. 3, 181-205. MR 0390516 (52:11341)
5.: A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer-Verlag, 1984. MR 0748308 (85e:35077)
6.: P. Marcati, A. Milani, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J. Differential Equations 84 (1990), no. 1, 129-147.MR 1042662 (91i:35156)
7.: T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Département de Mathématique, Université de Paris-Sud, Orsay, 1978.MR 0481578 (58:1690)
8.: T. C. Sideris, B. Thomases, and D. Wang, Long time behavior of solutions to the 3D compressible Euler equations with damping, Comm. Partial Differential Equations 28 (2003), no. 3-4, 795-816. MR 1978315 (2004d:35208)
9.: J. Simon, Compact sets in the space $L\sp p(0,T;B)$ , Ann. Mat. Pura Appl. (4) 146 (1987), 65-96.MR 0916688 (89c:46055)
10.: W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal. 172 (2004), no. 2, 247-266. MR 2058165 (2005c:35195)

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35L25, 35L65, 35L45, 76N15

Jean-François Coulombel
Affiliation: Team SIMPAF--INRIA Futurs, CNRS & Université Lille 1, Laboratoire Paul Painlevé, UMR CNRS 8524, Cité Scientifique, 59655 Villeneuve D'Ascq Cedex, France
Email: jfcoulom@math.univ-lille1.fr

Thierry Goudon
Affiliation: Team SIMPAF--INRIA Futurs, CNRS & Université Lille 1, Laboratoire Paul Painlevé, UMR CNRS 8524, Cité Scientifique, 59655 Villeneuve D'Ascq Cedex, France
Email: thierry.goudon@math.univ-lille1.fr

DOI: 10.1090/S0002-9947-06-04028-1
PII: S 0002-9947(06)04028-1
Keywords: Gas dynamics, relaxation, global smooth solutions
Received by editor(s): November 19, 2004
Posted: July 21, 2006
Additional Notes: The research of the authors was supported by the EU financed network HYKE, HPRN-CT-2002-00282.
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS