On an Initial-boundary Value Problem Which Arises in the Dynamics of a Compressible Ideal Stratified Fluid

Abstract

In this paper, we investigate the problem on small motions of a compressible ideal stratified fluid in a bounded domain. The problem is studied on the base of approach connected with application of so-called operator matrices theory, as well as abstract differential operator equations. For this purpose, Hilbert spaces and some of their subspaces are introduced. The original initial-boundary value problem reduces to the Cauchy problem for a second-order differential operator equation in the orthogonal sum of some Hilbert spaces. Further, an equation with a closed operator is associated with the resulting equation. On this basis, sufficient conditions for the existence of a solution to the corresponding problem are found.

Keywords

• compressible stratified fluid
• initial boundary value problem