Dissipative Boussinesq equations on non-cylindrical domains in R^n

Abstract

This article concerns the initial-boundary value problem for the nonlinear Boussinesq equations on time dependent domains in $mathbb{R}^n$ with $1leq n leq 4$. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded in some sense.

Keywords

• Boussinesq equation
• time dependent domains
• existence
• uniqueness
• asymptotic behavior