Abstract
Abstract This article studies the partial vanishing viscosity limit of the 2D Boussinesq system in a bounded domain with a slip boundary condition. The result is proved globally in time by a logarithmic Sobolev inequality. 2010 MSC: 35Q30; 76D03; 76D05; 76D07.
Highlights
Let Ω ⊂ R2 be a bounded, connected domain with smooth boundary ∂Ω, and n is the unit outward normal vector to ∂Ω
When θ = 0, the Boussinesq system reduces to the well-known Navier-Stokes equations
Testing (1.1) by u, using (1.2), (1.4), and (2.1), we find that
Summary
Introduction Let Ω ⊂ R2 be a bounded, connected domain with smooth boundary ∂Ω, and n is the unit outward normal vector to ∂Ω. U · n = 0, curlu = 0, θ = 0, on ∂ × (0,∞), (1:4) The aim of this article is to study the partial vanishing viscosity limit ® 0. When θ = 0, the Boussinesq system reduces to the well-known Navier-Stokes equations.
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