Global existence and uniqueness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity

2024/03/01 by Jiu, Quansen, Ma, Lin, Wang, Fengchao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.00309

Abstract

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial horizontal velocity is suitably small, that is, ‖∇ u₀‖_L²≤ η₀ for suitably small η₀>0. The initial data may contain vacuum. The proof is based on the local well-posedness and the blow-up criterion proved in \cite0, which states that if T^* is the maximal existence time of the local strong solutions (ρ,u,w,P) and T^*<∞, then \beginequation* sup_0≤ t

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