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On the analyticity of periodic gravity water waves with integrable vorticity function. (English) Zbl 1324.76008

The paper deals with the regularity properties of periodic gravity water waves traveling over a flat bed when gravity is the sole driving mechanism. The waves are considered to be rotational. Assuming integrability of the vorticity function the authors prove real-analyticity of the free surface and of the streamlines for solutions of the weak formulation of the water wave problem derived in [A. Constantin and W. Strauss, Arch. Ration. Mech. Anal. 202, No. 1, 133–175 (2011; Zbl 1269.76024)]. The proof of the main result (Theorem 1.1) combines the invariance of the problem with respect to horizontal translations with the Schauder estimates for weak solutions of elliptic boundary value problems.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q31 Euler equations
76B47 Vortex flows for incompressible inviscid fluids

Citations:

Zbl 1269.76024
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