Well-posedness of the water-wave with viscosity problem

2020/03/25 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.2003.11454

Abstract

In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other hand, we establish the global well-posedness in Wiener spaces for a sufficiently large viscosity. These results are the first rigorous proofs of well-posedness for the Dias, Dyachenko & Zakharov system (\em Physics Letters A 2008) modelling gravity waves with viscosity when surface tension is not taken into account.

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