Free boundary value problem for damped Euler equations and related models with vacuum

This paper is concerned with the local well-posedness for the free boundary value problem of smooth solutions to the cylindrical symmetric Euler equations with damping and related models, including the compressible Euler equations and the Euler-Poisson equations. The free boundary is moving in the r...

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Bibliographic Details
Published in:Journal of Differential Equations 2022-06, Vol.321, p.349-380
Main Authors: Meng, Rong, Mai, La-Su, Mei, Ming
Format: Article
Language:English
Subjects:
Compressible Euler equations
Euler equations with damping
Euler-Poisson equations
Free boundary
Local smooth solutions
Vacuum
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Summary:This paper is concerned with the local well-posedness for the free boundary value problem of smooth solutions to the cylindrical symmetric Euler equations with damping and related models, including the compressible Euler equations and the Euler-Poisson equations. The free boundary is moving in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. However, the compressible Euler equations or Euler-Poisson equations with damping become a degenerate system at the moving boundary. By setting a suitable weighted Sobolev space and using Hardy's inequality, we successfully overcome the singularity at the center point and the vacuum occurring on the moving boundary, and obtain the well-posedness of local smooth solutions. We also summarize the recent related results on the free boundary value problem for the Euler equations with damping, compressible Euler equations and Euler-Poisson equations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.03.014