Abstract
We study the beach problem for water waves. The case we consider is a compact fluid domain, where the free surface intersects the bottom along an edge, with a non-zero contact angle. Using elliptic estimates in domains with edges and a new equation on the Taylor coefficient, we establish a priori estimates for angles smaller than a dimensional constant. Local existence will be derived in a following paper.
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Communicated by N. Masmoudi
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de Poyferré, T. A Priori Estimates for Water Waves with Emerging Bottom. Arch Rational Mech Anal 232, 763–812 (2019). https://doi.org/10.1007/s00205-018-01333-w
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DOI: https://doi.org/10.1007/s00205-018-01333-w