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Initial-boundary value problem for two-dimensional viscous Boussinesq equations. (English) Zbl 1231.35171
In the paper under review the authors study the initial boundary value problem of two-dimensional viscous Boussinesq equations over a bounded domain with smooth boundary. They show that the equations have unique classical solution for \(H^3\) initial data and no-slip boundary condition. In addition, the authors show that the kinetic energy is uniformly bounded in time.

35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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