Well-posedness of water wave model with viscous effects

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URI: https://hdl.handle.net/10902/29600
ISSN: 0002-9939
ISSN: 1088-6826
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Autoría
Granero Belinchón, RafaelAutoridad Unican; Scrobogna, Stefano
Fecha
2020-12
Derechos
© American Mathematical Society. First published in Proceedings of the American Mathematical Society in 2020 148(12), published by the American Mathematical Society
Publicado en
Proceedings of the American Mathematical Society, 2020, 148, 5181-5191
Editorial
American Mathematical Society
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Resumen/Abstract
Starting from the paper by Dias, Dyachenko, and Zakharov (Physics Letters A, 2008) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with or without surface tension effects. This equation takes the form of a nonlocal fourth order wave equation and retains the main contributions to the dynamics of the free surface. Then, we prove the well-posedness in Sobolev spaces of such an equation.
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