Solvability of the First Initial-boundary Value Problem for the Quasihydrodynamics Equations in the Shallow Water Approximation

The unique solvability of an analog of the first initial boundary value problem for the quasihydrodynamics equations in the shallow water approximation is established under certain conditions on the data. A solution is regular , i.e., all generalized derivatives occurring in the equation are summable to some power. The proof relies on a priori estimates and the contraction mapping principle.