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Dissipative Boussinesq equations on non-cylindrical domains in $$\mathbb R^n$$. (English) Zbl 1184.35054
Summary: This article concerns the initial-boundary value problem for the nonlinear Boussinesq equations on time dependent domains in $$\mathbb{R}^n$$ with $$1\leq n \leq 4$$. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded in some sense.
##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35Q35 PDEs in connection with fluid mechanics
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