Large time decay of solutions to isentropic gas dynamics
Author:
Naoki Tsuge
Journal:
Quart. Appl. Math. 65 (2007), 135-143
MSC (2000):
Primary 35L65, 35L60, 76J20
DOI:
https://doi.org/10.1090/S0033-569X-06-01043-6
Published electronically:
December 14, 2006
Full-text PDF Free Access
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
- Alberto Bressan, Hyperbolic systems of conservation laws, Oxford Lecture Series in Mathematics and its Applications, vol. 20, Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. MR 1816648
- G.-Q. Chen, The compensated compactness method and the system of isentropic gas dynamics, MSRI preprint 00527-91, Berkeley (1990).
- Xia Xi Ding, Gui Qiang Chen, and Pei Zhu Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. I, II, Acta Math. Sci. (English Ed.) 5 (1985), no. 4, 415–432, 433–472. MR 922139, DOI https://doi.org/10.1016/S0252-9602%2818%2930542-3
- Benoît Perthame, Kinetic formulation of conservation laws, Oxford Lecture Series in Mathematics and its Applications, vol. 21, Oxford University Press, Oxford, 2002. MR 2064166
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
References
- A. Bressan, Hyperbolic Systems of Conservation Laws, (Oxford University Press, 2000). MR 1816648 (2002d:35002)
- G.-Q. Chen, The compensated compactness method and the system of isentropic gas dynamics, MSRI preprint 00527-91, Berkeley (1990).
- 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)
- B. Perthame, Kinetic formulation of conservation laws. Oxford Lecture Series in Mathematics and its Applications, 21., (Oxford University Press, Oxford, 2002). MR 2064166
- J. Smoller, Shock Waves and Reaction-Diffusion Equations, (Springer-Verlag, New York, 1983). MR 0688146 (84d:35002)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
35L65,
35L60,
76J20
Retrieve articles in all journals
with MSC (2000):
35L65,
35L60,
76J20
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
Keywords:
Isentropic gas dynamics,
decay,
the Lax-Friedrichs scheme.
Received by editor(s):
March 30, 2006
Published electronically:
December 14, 2006
Additional Notes:
The author was supported in part by JSPS Research Fellowships for Young Scientists.
Article copyright:
© Copyright 2006
Brown University
