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In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.
In a recent paper , Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B 2 2,1. In the present paper we prove that the Navier-Stokes system is globally well-posed in B 2 2,1 , with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L 2 is of… (More)