Abstract
In this paper we prove the global well-posedness for the Three dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier-Stokes equation with vanishing the horizontal viscosity with a transport-diffusion equation governing the temperature.
Highlights
Boussinesq system are widely used to model the dynamics of the ocean or the atmosphere
Rousset proved the global well-posedness for the Navier-Stokes- Boussinesq system with axisymmetric data by virtue of the structure of the coupling between two equations of (1.1) with ν1 = ν2 and κ1 = κ2
Rousset prove the global well-posedness for the threedimensional Euler-Boussinesq system with axisymmetric initial data without swirl in
Summary
Boussinesq system are widely used to model the dynamics of the ocean or the atmosphere. Note that when the initial density ρ0 is identically zero (or constant) and ν1 = ν2 the above system is reduced to the classical incompressible Navier-Stokes equation. This system has been studied by many authors due to his physical background and mathematical significance. There is little study about the global well-posedness result for large initial data, even for the threedimensional Navier-Stokes equations. Rousset proved the global well-posedness for the Navier-Stokes- Boussinesq system with axisymmetric data by virtue of the structure of the coupling between two equations of (1.1) with ν1 = ν2 and κ1 = κ2. Rousset prove the global well-posedness for the threedimensional Euler-Boussinesq system with axisymmetric initial data without swirl in
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