On the physical vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation

被引:0
作者
Li, Kelin [1 ]
Wang, Yuexun [1 ]
机构
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
关键词
NAVIER-STOKES EQUATIONS; COMPRESSIBLE EULER EQUATIONS; NONLINEAR ASYMPTOTIC STABILITY; LOCAL WELL-POSEDNESS; LANE-EMDEN SOLUTIONS; GLOBAL EXISTENCE; SMOOTH SOLUTIONS; BLOW-UP; VISCOSITY; SYSTEM;
D O I
10.1063/5.0196542
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
This paper is concerned with the vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation. We establish the local-in-time well-posedness of classical solutions to this system, and the solutions possess higher-order regularity all the way to the vacuum free boundary, though the density degenerates near the vacuum boundary. To deal with the force term generated by the Poisson equation, we make use of the structure of the momentum equation formulated in a fixed domain by the Lagrangian coordinates. The proof is built on some higher-order weighted energy functionals and weighted embeddings corresponding to the degeneracy near the initial vacuum boundary.
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页数:24
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