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Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data. (English) Zbl 1200.35229
Summary: We prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier-Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient \(\kappa \geq 0\) which may vanish.

MSC:
35Q35 PDEs in connection with fluid mechanics
76R50 Diffusion
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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