Research and Innovation Articles
Global Existence and Stability to the Isothermal Gas Dynamics System with an Outer Force
Published 2020-11-20
Keywords
- Global L∞ solution,
- isothermal system,
- outer force,
- flux approximation,
- compensated compactness
How to Cite
Wang, X. T., Lu, Y. G., & Rendón, L. (2020). Global Existence and Stability to the Isothermal Gas Dynamics System with an Outer Force. Revista Integración, Temas De matemáticas, 38(2), 103–108. https://doi.org/10.18273/revint.v38n2-2020003
Copyright (c) 2020 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
In this paper, we apply the classical viscosity method, coupled with the flux approximation and the compensated compactness theory to obtain the global existence of the bounded entropy solutions for the isothermal gas dynamics system with an outer source. The a-priori time-independent L∞ estimates are proved by applying the maximum principle to a suitable nonlinear coupled parabolic system of two equations.
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References
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Hu Y.-B., Lu Y.-G. and Tsuge N., “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force”, Appl. Math. Lett., 95 (2019), 36-40. doi: 10.1016/j.aml.2019.03.022.
Huang F.-M. and Wang Z., “Convergence of Viscosity Solutions for Isentropic Gas Dynamics”, SIAM J. Math. Anal., 34 (2003), No. 3, 595-610. doi: 10.1137/S0036141002405819.
Lions P.L., Perthame B. and Souganidis P. E., “Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates”, Comm. Pure Appl. Math., 49 (1996), No. 6, 599-638. doi: 10.1002/(SICI)1097- 0312(199606)49:6%3C599::AID-CPA2%3E3.0.CO;2-5.
Lions P.L., Perthame B. and Tadmor E., “Kinetic formulation of the isentropic gas dynamics and p-system”, Commun. Math. Phys., 163 (1994), No. 2, 415-431. doi: 10.1007/BF02102014.
Lu Y.-G., “Global Existence of Resonant Isentropic Gas Dynamics”, Nonlinear Anal. Real World Appl., 12 (2011), No. 5, 2802-2810. doi: 10.1016/j.nonrwa.2011.04.005.
Lu Y.-G., “Some Results on General System of Isentropic Gas Dynamics”, Differential Equations, 43 (2007), No. 1, 130-138. doi: 10.1134/S0012266107010132.
Lu Y.-G., “Global Hölder continuous solution of isentropic gas dynamics”, Proc. Royal Soc. Edinburgh, 123 (1993), No. 2, 231-238. doi: 10.1017/S0308210500025658.
Murat F., “Compacité par compensation”, Ann. Sc. Norm. Super. Pisa, 5 (1978), 489-507.
Nishida T., “Global solution for an initial-boundary-value problem of a quasilinear hyperbolic system”, Proc. Jap. Acad., 44 (1968), No. 7, 642-646. doi: 10.3792/pja/1195521083.
Tartar L.C., Compensated compactness and applications to partial differential equations, Research Notes in Mathematics, London, 1979.
Whitham G. B., Linear and Nonlinear Waves, Wiley, New York, 1974.