On a regularization of the compressible Euler equations for an isothermal gas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:358

Article

Bhat, H. S.¹  Fetecau, R. C.² 

[1] Univ Calif Merced, Sch Nat Sci, Merced, CA 95344 USA

[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

关键词: Compressible Euler equations;    Leray regularization;    Riemann invariants;    Isothermal gas;   

DOI  :  10.1016/j.jmaa.2009.04.051

来源: Elsevier

【 摘 要 】

We consider a Leray-type regularization of the compressible Euler equations for an isothermal gas. The regularized system depends on a small parameter alpha > 0. Using Riemann invariants, we prove the existence of smooth solutions for the regularized system for every alpha > 0. The regularization mechanism is a non-linear bending of characteristics that prevents their finite-time crossing. We prove that, in the alpha -> 0 limit, the regularized solutions converge strongly. However, based on our analysis and numerical simulations, the limit is not the unique entropy solution of the Euler equations. The numerical method used to support this claim is derived from the Riemann invariants for the regularized system. This method is guaranteed to preserve the monotonicity of characteristics. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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