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2D inviscid heat conductive Boussinesq equations on a bounded domain. (English) Zbl 1205.35048
The author considers 2D inviscid heat convective Boussinesq equations in a domain with smooth boundary. The question of global regularity/finite time singularity for the case of $$\nu = 0$$ and $$k > 0$$ is still open. The author gives a definite answer to this question in this paper. The author proves that there exists a unique global smooth solution Boussineq equation for smooth initial data. The temperature converges exponentially to its boundary value as time goes to infinity, and the velocity and vorticity are uniformly bounded in time.

##### MSC:
 35G61 Initial-boundary value problems for systems of nonlinear higher-order PDEs 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids
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##### References:
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