Quarterly of Applied Mathematics

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Large time decay of solutions to isentropic gas dynamics

Author(s): Naoki Tsuge
Journal: Quart. Appl. Math. 65 (2007), 135-143.
MSC (2000): Primary 35L65, 35L60, 76J20
Posted: December 14, 2006
MathSciNet review: 2313152
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Abstract | References | Similar articles | Additional information

Abstract: We study the large time behavior of solutions to isentropic gas dynamics. For a constant $\gamma$ $(1<\gamma<3)$ , we show the decay of the $L^{\gamma}$ norm of density. To do this, we estimate approximate solutions constructed by a difference scheme.

References:

1.: A. Bressan, Hyperbolic Systems of Conservation Laws, (Oxford University Press, 2000). MR 1816648 (2002d:35002)
2.: G.-Q. Chen, The compensated compactness method and the system of isentropic gas dynamics, MSRI preprint 00527-91, Berkeley (1990).
3.: X. Ding, G.-Q. Chen and P. Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II), Acta Mathematica Scientia 7 (1987), 467-480, 8 (1988), 61-94 (in Chinese), 5 (1985), 415-432, 433-472 (in English). MR 0922139 (89f:76006)
4.: B. Perthame, Kinetic formulation of conservation laws. Oxford Lecture Series in Mathematics and its Applications, 21., (Oxford University Press, Oxford, 2002). MR 2064166
5.: J. Smoller, Shock Waves and Reaction-Diffusion Equations, (Springer-Verlag, New York, 1983). MR 0688146 (84d:35002)

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Additional Information:

Naoki Tsuge
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Osaka 560-0043, Japan
Email: tuge@math.sci.osaka-u.ac.jp
PII: S0033-569X-06-01043-6
Keywords: Isentropic gas dynamics, decay, the Lax-Friedrichs scheme.
Received by editor(s): March 30, 2006
Posted: December 14, 2006
Additional Notes: The author was supported in part by JSPS Research Fellowships for Young Scientists.
Copyright of article: Copyright 2006, Brown University

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