@Article{CMAA-1-3,
author = {Wei, Wang and Zhifei, Zhang 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 = {<p style="text-align: justify;">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.</p>},
issn = {2790-1939},
doi = {https://doi.org/2022-CMAA-20663},
url = {https://global-sci.com/article/81436/well-posedness-of-the-free-boundary-problem-for-the-compressible-euler-equations-and-the-incompressible-limit}
}