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Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation. (English) Zbl 1300.35108
Summary: The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal diffusion. Attention is focused on the case when the thermal diffusion dominates. We establish the global well-posedness for the 2D Boussinesq equations with a new range of fractional powers of the Laplacian.

MSC:
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
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