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

• Published in: Нелінійні коливання
• Date: 2001
• Main Author: Zolotenko, G.F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2001
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/174760
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On solutions of general nonlinear initial boundary-value problem of inviscid fluid's dynamics in moving vessel / G.F. Zolotenko // Нелінійні коливання. — 2001. — Т. 4, № 4. — С. 560-573. — Бібліогр.: 11 назв. — англ.

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.