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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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