Free boundary value problem for damped Euler equations and related models with vacuum
Free boundary value problem for damped Euler equations and related models with vacuum
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DOI：
10.1016/j.jde.2022.03.014
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发表时间：
2022-06
影响因子：
2.4
通讯作者：
Rong Meng;La-Su Mai;Ming Mei
中科院分区：
文献类型：
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作者：
Rong Meng;La-Su Mai;Ming Mei
本文讨论了带阻尼柱对称Euler方程及其相关模型，包括可压缩Euler方程和Euler-Poisson方程的光滑解的自由边值问题的局部适定性。自由边界随着径向速度沿径向移动，这会影响角速度，但不会影响轴向速度。然而，带阻尼项的可压缩Euler方程或Euler-Poisson方程在运动边界处成为退化系统。通过设置适当的加权Soblev空间并利用Hardy不等式，我们成功地克服了运动边界上出现的中心奇性和真空，并获得了局部光滑解的适定性。我们还总结了最近关于含阻尼欧拉方程、可压缩欧拉方程和欧拉-泊松方程的自由边值问题的相关结果。
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.