Abstract
In this paper, we consider the solvability, regularity and vanishing viscosity limit of the 3D viscous Boussinesq equations with a Navier-slip boundary condition. We also obtain the rate of convergence of the solution of viscous Boussinesq equations to the corresponding ideal Boussinesq equations.
Highlights
1 Introduction Let Ω ⊂ R3 be a class of bounded smooth domains
We investigate the 3D Boussinesq equations, which are governed by the following equations:
As ν, k → 0, (u, θ ) converges to the unique solution (u0, θ 0) of the ideal Boussinesq equations with the same initial data in the sense that u(ν, k), θ (ν, k) → u0, θ 0 in L2(0, T; W ), (2019) 2019:177
Summary
Let Ω ⊂ R3 be a class of bounded smooth domains. We investigate the 3D Boussinesq equations, which are governed by the following equations:. We follow the approach of [6, 7] and formulate the boundary value problem in a suitable functional setting so that the Stokes operator is well behaved. The nonlinear terms naturally fall into desired functional spaces These facts allow us to establish the existence and regularity of solutions through the Galerkin approximation and appropriate a priori bounds. Theorem 4.1 Let (u0, θ0) ∈ V , we have T∗ > 0, depending on ν, k, and the H1-norm of (u0, θ0) only such that (1.1)–(1.5) has a unique strong solution (u, θ ) on [0, T∗) satisfying (u, θ ) ∈ L2(0, T; W ) ∩ C 0, T∗; V u , θ ∈ L2(0, T; V ), for any T ∈ (0, T∗).
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