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Well-posedness of water wave model with viscous effects

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.

 Fuente: Proceedings of the American Mathematical Society, 2020, 148, 5181-5191

 Editorial: American Mathematical Society

 Fecha de publicación: 01/12/2020

 Nº de páginas: 11

 Tipo de publicación: Artículo de Revista

 DOI: 10.1090/proc/15219

 ISSN: 0002-9939,1088-6826

 Proyecto español: MTM2017-89976-P

 Url de la publicación: https://doi.org/10.1090/proc/15219