期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 51, 期 3, 页码 1913-1964出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1211994
关键词
compressible primitive equations; atmospheric dynamics; weak solutions; degenerate viscosity
资金
- Ecole Polytechnique Foundation
- ONR [N00014-15-1-2333]
- Einstein Stiftung/Foundation - Berlin
- John Simon Guggenheim Memorial Foundation
We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compressible Navier-Stokes equations, the weak solutions satisfy the basic energy inequality, the Bresh-Desjardins entropy inequality, and the Mellet-Vasseur estimate. These estimates play an important role in establishing the compactness of the vertical velocity of the approximating solutions, and therefore are essential to recover the vertical velocity in the weak solutions.
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