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A Nash-Moser theorem for standing water waves. (English) Zbl 0991.76010

Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1379-1384 (2000).
From the summary: We use Nash-Moser iteration to construct small-amplitude standing water waves given by solutions of Euler’s equation for an irrotational incompressible flow with exact nonlinear boundary conditions. The small-divisor problem which dominates the theory is confronted by seeking only waves which satisfy certain a priori constraints on the normal component of pressure gradient at the free surface.
For the entire collection see [Zbl 0949.00026].

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B07 Free-surface potential flows for incompressible inviscid fluids
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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