The second variation of the stream function energy of water waves with vorticity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Weiss, Georg S.¹  Zhang, Guanghui¹ 

[1] Univ Dusseldorf, Math Inst, D-40225 Dusseldorf, Germany

关键词: Water wave;    Stagnation point;    Singularity;    Second variation;    Stokes corner;   

DOI  :  10.1016/j.jde.2012.07.005

来源: Elsevier

【 摘 要 】

We compute the second variation of the stream function energy of two-dimensional steady free surface gravity water waves with vorticity in the stream function formulation. We prove that for nonpositive vorticity the second variation of the stream function energy at extreme waves with Stokes corner asymptotics cannot be nonnegative in any small neighbourhood of a given isolated stagnation point. The particular form of our second variation suggests however the possibility that certain singularities in the case of nonzero vorticity might be constructible as minimizers of the stream function energy. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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