Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities

DOI10.1137/18M1211994zbMath1419.35150arXiv1808.03975MaRDI QIDQ5231298

Xin Liu, Edriss S. Titi

Publication date: 26 August 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03975

zbMATH Keywords

weak solutionscompressible primitive equationsatmospheric dynamicsdegenerate viscosity

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (16)

Global well-posedness of z-weak solutions to the primitive equations without vertical diffusivity ⋮ 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 ⋮ The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations ⋮ 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 well‐posedness of the 3D primitive equations with only horizontal eddy diffusivity and delays in both convective and heat source terms ⋮ Global existence of weak solutions to 3D compressible primitive equations with degenerate viscosity ⋮ Global existence and asymptotic stability of the free boundary problem of the primitive equations with heat insulation ⋮ Blow-up criterion of solutions of the horizontal viscous primitive equations with horizontal eddy diffusivity ⋮ Local existence and uniqueness of strong solution to the inhomogeneous primitive equations with vacuum ⋮ Global existence of weak solutions to the Navier-Stokes-Korteweg equations ⋮ Global well-posedness of strong solutions to the 2D nonhomogeneous incompressible primitive equations with vacuum ⋮ 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 ⋮ Global well-posedness of the three-dimensional viscous primitive equations with bounded delays

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