Existence of a global weak solution to compressible primitive equations

DOI10.1016/j.crma.2012.04.013zbMath1253.35119OpenAlexW1990778254MaRDI QIDQ424748

Mehmet Ersoy, Timack Ngom

Publication date: 4 June 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/581

zbMATH Keywords

a priori estimatecompressible primitive equationsglobal weak existence

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

Related Items (13)

Local existence and uniqueness of strong solutions to the two dimensional nonhomogeneous incompressible primitive equations ⋮ On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations-rigorous justification ⋮ Incompressible limit of the compressible primitive equations with gravity: well-prepared initial data ⋮ On weak-strong uniqueness and singular limit for the compressible primitive equations ⋮ Zero Mach number limit of the compressible primitive equations: well-prepared initial data ⋮ Global existence of weak solutions to 3D compressible primitive equations with degenerate viscosity ⋮ Local existence and uniqueness of strong solution to the inhomogeneous primitive equations with vacuum ⋮ On the stability of weak solution for compressible primitive equations ⋮ Uniqueness of the global weak solutions to 2D compressible primitive equations ⋮ Local well-posedness of strong solutions to the three-dimensional compressible primitive equations ⋮ Local existence and uniqueness of strong solutions to the two dimensional compressible primitive equations with density-dependent viscosity ⋮ Dimension reduction for compressible pipe flows including friction ⋮ Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities

Cites Work

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• Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects
• Compressible primitive equations: formal derivation and stability of weak solutions
• New formulations of the primitive equations of atmosphere and applications
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation

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