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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.

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