Well-posedness of a water wave model with viscous effects

2019/11/05 by Granero-Belinchón, Rafael, Scrobogna, Stefano
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.1911.01912

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 equation.

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