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Global regularity of solutions of 2D Boussinesq equations with fractional diffusion. (English) Zbl 1177.76024
Summary: The goal of this work is to study the Boussinesq equations for an incompressible fluid in \(\mathbb R^2\), with diffusion modeled by fractional Laplacian. The existence, the uniqueness and the regularity of solution has been proved.

MSC:
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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