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Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation. (English) Zbl 1200.35228
Summary: We study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
35R11 Fractional partial differential equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
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