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Volume 1, Issue 3
Well-Posedness of the Free Boundary Problem for the Compressible Euler Equations and the Incompressible Limit

Wei Wang, Zhifei Zhang & Wenbin Zhao

Commun. Math. Anal. Appl., 1 (2022), pp. 410-456.

Published online: 2022-06

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  • 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.

  • Keywords

Compressible Euler, free boundary, incompressible limit.

  • AMS Subject Headings

35Q31, 35Q35, 35R35, 76B03, 76N10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-1-410, author = {Wang , WeiZhang , Zhifei and Zhao , Wenbin}, title = {Well-Posedness of the Free Boundary Problem for the Compressible Euler Equations and the Incompressible Limit}, journal = {Communications in Mathematical Analysis and Applications}, year = {2022}, volume = {1}, number = {3}, pages = {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.

}, issn = {2790-1939}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmaa/20663.html} }
TY - JOUR T1 - Well-Posedness of the Free Boundary Problem for the Compressible Euler Equations and the Incompressible Limit AU - Wang , Wei AU - Zhang , Zhifei AU - Zhao , Wenbin JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 410 EP - 456 PY - 2022 DA - 2022/06 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmaa/20663.html KW - Compressible Euler, free boundary, incompressible limit. AB -

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.

Wang , WeiZhang , Zhifei and Zhao , Wenbin. (2022). Well-Posedness of the Free Boundary Problem for the Compressible Euler Equations and the Incompressible Limit. Communications in Mathematical Analysis and Applications. 1 (3). 410-456. doi:
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