Global well-posedness for 2D Boussinesq system with general supercritical dissipation
The authors consider a Cauchy problem of the 2D incompressible generalized Boussinesq equations with the fractional Laplacian dissipation, for the velocity vector field, the pressure and the temperature. This system is associated to the Zygmund operator and to other operator defined by the Fourier transform. The Boussinesq system is a model to describe the geophysical flows, such as oceanic circulation and atmospheric fronts and is similar to the 2D incompressible Navier-Stokes system. In the supercritical case, the authors established the local well-posedness results for the Boussinesq system with suitable initial data and gave two blow-up criteria in terms of velocity and temperature. The main aim of this paper is to obtain a blow-up criteria better than previous and to prove the global well-posedness result with the small initial data. The results are obtained by using the Fourier localization method.
scientific article; zbMATH DE number 6523605
scientific article