Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity

Authors

  • Jules Ouya
  • Arouna Ouedraogo Université Norbert Zongo

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i4.4931

Keywords:

compressible primitive equations, global weak solutions, degenerate viscosity density-dependent

Abstract

In this work, we show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosity density-dependent for large initial data. With a pressure law of the form ρ2, we represent the vertical velocity as a function of the density and the horizontal one which will be important in using Faedo-Galerkin method to obtain the global existence of the approximate solutions. In analogy with the cases in [28] and [26, 27], we prove that the weak solutions satisfy the basic energy inequality and the Bresch-Desjardins entropy inequality. Based on these estimates and using compactness arguments, we prove the global existence of weak solutions of (1.1) by vanishing the parameters in our approximate system step by step.

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Published

2023-10-30

Issue

Section

Nonlinear Analysis

How to Cite

Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity. (2023). European Journal of Pure and Applied Mathematics, 16(4), 2247-2285. https://doi.org/10.29020/nybg.ejpam.v16i4.4931