Well-posedness of water wave model with viscous effects

Granero-Belinchón, Rafael; Scrobogna, Stefano

doi:10.1090/proc/15219

Well-posedness of water wave model with viscous effects

Authors: Rafael Granero-Belinchón and Stefano Scrobogna
Journal: Proc. Amer. Math. Soc. 148 (2020), 5181-5191
MSC (2010): Primary 35Q35, 35R35, 35Q31, 35L25
DOI: https://doi.org/10.1090/proc/15219
Published electronically: September 18, 2020
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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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