Characteristic properties of the system of equations of a shear flow with nonmonotonic velocity profile

Abstract

We consider the initial boundary value problem with a free boundary. The problems is described in the paper the long-wave theory approximation, the plane-parallel vortex flow of a layer of a homogeneous liquid at a depth H = H(X, T) above an even bottom Y = O in a gravity field, Here U, V are components of the vector of the liquid velocity, p is the pressure, {rho} is the density ({rho} = const), g is the acceleration of gravity, and U{sub 0}(X, Y), H{sub 0}(X) are prescribed functions.