On a regularization of the compressible Euler equations for an isothermal gas |
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Authors: | HS Bhat RC Fetecau |
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Institution: | a School of Natural Sciences, University of California, Merced, 5200 N. Lake Rd., Merced, CA 95344, USA b Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada |
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Abstract: | We consider a Leray-type regularization of the compressible Euler equations for an isothermal gas. The regularized system depends on a small parameter α>0. Using Riemann invariants, we prove the existence of smooth solutions for the regularized system for every α>0. The regularization mechanism is a non-linear bending of characteristics that prevents their finite-time crossing. We prove that, in the α→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. |
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Keywords: | Compressible Euler equations Leray regularization Riemann invariants Isothermal gas |
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