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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 (Physics Letters A2008) modelinggravity waves with viscosity when surface tension is not taken into account.
Fuente: Journal of differential equations, 2021, 276, 96-148
Publisher: Elsevier
Publication date: 01/03/2021
No. of pages: 53
Publication type: Article
DOI: 10.1016/j.jde.2020.12.019
ISSN: 1090-2732,0022-0396
Spanish project: MTM2017-82184-R
Publication Url: https://doi.org/10.1016/j.jde.2020.12.019
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RAFAEL GRANERO BELINCHON
SCROBOGNA , STEFANO
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