Well-posedness of the water-wave with viscosity problem

Granero Belinchón, Rafael; Scrobogna, Stefano

doi:10.1016/j.jde.2020.12.019

dc.contributor.author	Granero Belinchón, Rafael
dc.contributor.author	Scrobogna, Stefano
dc.contributor.other	Universidad de Cantabria	es_ES
dc.date.accessioned	2023-08-04T12:47:03Z
dc.date.available	2023-08-04T12:47:03Z
dc.date.issued	2021-03
dc.identifier.issn	1090-2732
dc.identifier.issn	0022-0396
dc.identifier.other	MTM2017-82184-R	es_ES
dc.identifier.other	MTM2017-89976-P	es_ES
dc.identifier.other	PID2019-109348GA-I00	es_ES
dc.identifier.uri	https://hdl.handle.net/10902/29599
dc.description.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.	es_ES
dc.description.sponsorship	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.	es_ES
dc.format.extent	36 p.	es_ES
dc.language.iso	eng	es_ES
dc.publisher	Elsevier	es_ES
dc.rights	© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license	es_ES
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.source	Journal of differential equations, 2021, 276, 96-148	es_ES
dc.subject.other	Damped water waves	es_ES
dc.subject.other	Viscosity	es_ES
dc.subject.other	Well-posedness	es_ES
dc.subject.other	Cross-diffusion system	es_ES
dc.title	Well-posedness of the water-wave with viscosity problem	es_ES
dc.type	info:eu-repo/semantics/article	es_ES
dc.relation.publisherVersion	https://doi.org/10.1016/j.jde.2020.12.019	es_ES
dc.rights.accessRights	openAccess	es_ES
dc.identifier.DOI	10.1016/j.jde.2020.12.019
dc.type.version	acceptedVersion	es_ES