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Analyticity of rotational traveling gravity two‐layer waves
Author(s) -
Chu Jifeng,
Wang LingJun
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12358
Subject(s) - streamlines, streaklines, and pathlines , vorticity , flow (mathematics) , mathematical analysis , function (biology) , mathematics , stream function , bounded function , classical mechanics , physics , mechanics , vortex , evolutionary biology , biology
The aim of this paper is to prove real analytic properties of all streamlines of two‐dimensional steady rotational gravity water waves in two‐layer flows. Provided that there are no stagnation points in the flow, we show that each streamline, including the free surface and the interface, is a real analytic curve if the height function is in W l o c 2 , ∞ , which corresponds to an arbitrarily bounded and measurable vorticity function. Our results generalize those for the situation of single layer flow, and improve the results in the work by Chu, Escher, and Wang [Analyticity of rotational travelling waves in two‐layer flows, submitted], where the analyticity is obtained for rotational two‐layer water waves when the height function is in C 2 , αcorresponding to a Hölder continuous vorticity function.