On the Existence, Uniqueness, Stabilization and Limit Amplitude for Non-homogeneous System Modelling Internal Non-stationary Waves in Stratified Flows

摘要

A solution of the Cauchy problem for a general case of a non-homogeneous system of an exponentially stratified fluid in the gravity field is obtained in the form of singular integrals, taken in the Cauchy principal value sense, when singularities are removed by a ball, that is, isotropically. The exact exact Lp estimates (p> 1) are obtained for the solution. The existence and uniqueness theorems are proved. We also prove that for t →∞, for the solution of the Cauchy problem with homogeneous initial conditions for the case when the right side depends on time harmonically (F(x, t) = f(x)e-iwt), the stabilization takes place and the solution describes the mode of the induced vibrations with frequency W.