2009 Fiscal Year Final Research Report

Mathematical analysis on overhanging waves

Research Project

Project/Area Number	20740080
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	Basic analysis
Research Institution	Tokyo University of Science
Principal Investigator	OGAWA Masao Tokyo University of Science, 理工学部, 助教 (50408704)
Project Period (FY)	2008 – 2009
Keywords	非線形偏微分方程式
Research Abstract	The motion of water waves is a prime research subject in fluid dynamics. This motion is usually formulated as the free boundary problem for an irrotational, incompressible and ideal fluid. It is known that the temporally local solution for this problem exists, even if the waves overhang. On the other hand, the motion of the waves of the ocean is rotational. Therefore, we are interested in the water-wave problem without the assumption of the irrotational motion. First, the author has analyzed the linearized problem. This problem is different from the one in the case that the amplitude of the surface is not large. After that, by the result for the linearized problem and the symmetry of the equations, the existence of the temporally local solution for the water-wave problem has been shown.

(4 results)