On solutions of general nonlinear initial boundary-value problem of inviscid fluid's dynamics in moving vessel

Abstract

The problem of integrating the Laplace equation in a changing 3-dimensional region, with the initial and boundary conditions, is investigated. The paper is mainly devoted to the problem arising in dynamics of an inviscid incompressible fluid which partially fills a moving vessel and is in irrotational absolute motion. In this case the considered space region is bounded by the rigid vessel’s walls and the unknown free surface of fluid. The boundary conditions consist of the Neyman conditions on the rigid walls and the nonlinear kinematic and dynamic conditions on the free surface. Besides, the condition of a constancy of the region’s volume is imposed. The concept of a solution of this problem is analyzed. One distinguishes a certain class of solutions and proves their existence. An example of such a solution is given.