A note on incompressible limit for compressible Euler equations |
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Authors: | Jiang Xu Wen‐An Yong |
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Affiliation: | 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People's Republic of China;2. Zhou Pei‐Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of China |
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Abstract: | This paper presents a simple justification of the classical low Mach number limit in critical Besov spaces for compressible Euler equations with prepared initial data. As the first step of this justification, we formulate a continuation principle for general hyperbolic singular limit problems in the framework of critical Besov spaces. With this principle, it is also shown that, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible Euler equations have smooth solutions, and the definite convergence orders are obtained. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | compressible Euler equations continuation principle Besov spaces |
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