Well-Posedness of the Free Boundary Problem for the Compressible Euler Equations and the Incompressible Limit
Year: 2022
Author: Wei Wang, Zhifei Zhang, Wenbin Zhao
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 3 : pp. 410–456
Abstract
In this paper, we study the free boundary problem of the compressible Euler equations in the Eulerian coordinates. By deriving the evolution equation of the free surface, we relate the Taylor stability condition to the hyperbolicity of this evolution equation. Our approach not only yields exact information of the free surface, but also gives a simple proof of the local well-posedness of the free boundary problem. This approach provides a unified framework to treat both compressible and incompressible free boundary problems. As a byproduct, we can also prove the incompressible limit.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-CMAA-20663
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 3 : pp. 410–456
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 47
Keywords: Compressible Euler free boundary incompressible limit.