Kinsey, Rafe H.; Wu, Sijue A priori estimates for two-dimensional water waves with angled crests. (English) Zbl 1402.35226 Camb. J. Math. 6, No. 2, 93-181 (2018). The authors study the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical well at a possibly non-right angle. Under the assumptions that the air has density zero, the fluid is inviscid, incompressible and irrotational, and the surface tension is zero, a low-regularity energy functional is constructed and an a priori estimate is deduced. It is worth to point out that these don’t require the strong Taylor stability criterion. And it seems that the a priori estimate remains valid for general periodic water wave equations. Reviewer: Cheng He (Beijing) Cited in 2 ReviewsCited in 17 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35B45 A priori estimates in context of PDEs 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:water wave equations; Riemann mapping coordinates; a priori estimates PDFBibTeX XMLCite \textit{R. H. Kinsey} and \textit{S. Wu}, Camb. J. Math. 6, No. 2, 93--181 (2018; Zbl 1402.35226) Full Text: DOI arXiv