On Some Properties of a Linearized Quasi-Hydrodynamical System of Equations

We examine well-posedness questions in the Sobolev spaces of a boundary value problem for a linearized quasi-hydrodynamical system of equations in the case of weakly-compressible fluid. The existence and uniqueness of generalized and regular solutions are proven under some conditions for the data. In the case of a generalized solution, we assume only smoothness assumption for the data. In the case of regular solutions, i.e., all generalized derivatives in the equation are summable to some power p, we impose also some additional conditions on the norms of the data.