@article{10902/29599,
year = {2021},
month = {3},
url = {https://hdl.handle.net/10902/29599},
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.},
organization = {The research of S.S. is supported by the Spanish Ministry of Economy and Competitiveness MINECO through the project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym ”DESFLU” and by the European Research Council through the Starting Grant project H2020-EU.1.1.-639227 FLUID-INTERFACE. R. G-B has been funded by the grant MTM2017-89976-P from the Spanish Ministry of Economy and Competitiveness MINECO and the grant PID2019- 109348GA-I00 from the Spanish Ministry of Science, Innovation and Universities MICIU.},
publisher = {Elsevier},
publisher = {Journal of differential equations, 2021, 276, 96-148},
title = {Well-posedness of the water-wave with viscosity problem},
author = {Granero Belinchón, Rafael and Scrobogna, Stefano},
}