Analyticity of rotational traveling capillary–gravity waves with critical layers. (February 2023)

• Record Type: Journal Article
• Authors: Wang, Ling-Jun
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 35Q31 -- 35J60 -- 76B15; Rotational flow -- Capillary–gravity traveling waves -- Critical layer -- Analyticity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113164
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish real analyticity of the free surface of a two-dimensional steady rotational flow of water with critical layers. The flow is acted upon by gravity and surface tension. We show that any W l o c 2, ∞ -regular free surface is analytic provided the vorticity distribution is analytic. In particular, the surface of a water flow with constant vorticity is analytic.