Mixed problem for the equation governing inertia-gravity waves in the Boussinesq approximation in a unbounded cylindrical domain

Abstract

The unique solvability of an initial-boundary value problem for the equation governing inertia-gravity waves in the Boussinesq approximation in an unbounded multidimensional cylindrical domain is studied. The existence and uniqueness of a weak solution is proved, and its asymptotic behavior at long times is analyzed. The proofs are based on the Green’s function constructed in explicit form for the corresponding stationary problem.