An elementary approach to the inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations
The authors prove that the weak solution \(u_{\nu}\) of the 3D Navier-Stokes equations converges in \(L^{\infty}(0,T;L^2(\Omega))\) to the solution of the corresponding Euler equations, as \(\nu \) tends to zero. The rate of converges strongly depends on the initial data. These facts are then used to show that the solution \((u_{\nu}, \rho_{\nu})\) of the 3D Boussinesq equations (without diffusion, with Navier type slip boundary conditions) approaches the solution of the Euler-Boussinesq equations.
scientific article; zbMATH DE number 6358117
scientific article