A Priori Estimates for Two-Dimensional Water Waves with Angled Crests.

Partial Differential Equations;Water Waves;Mathematics;Science;Mathematics

Kinsey, Rafe HandSmoller, Joel A. ;

University of Michigan

关键词: Partial Differential Equations;    Water Waves;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/108736/rkinsey_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We consider the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly non-trivial angle; our problem also covers interfaces with angled crests.We assume that the fluid is inviscid, incompressible, and irrotational, with no surface tension and with air density zero.We construct a low-regularity energy and prove a closed energy estimate for this problem. Our work differs from earlier work in that, in our case, only a degenerate Taylor stability criterion holds, with the inward-facing normal derivative of the pressure non-negative, instead of the strong Taylor stability criterion, which requires that the inward-facing normal derivative of the pressure be bounded below by a strictly positive constant.