## Well-posedness of water wave model with viscous effects

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- by Rafael Granero-Belinchón and Stefano Scrobogna
- Proc. Amer. Math. Soc.
**148**(2020), 5181-5191 - DOI: https://doi.org/10.1090/proc/15219
- Published electronically: September 18, 2020
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## 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 an equation.## References

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## Bibliographic Information

**Rafael Granero-Belinchón**- Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avenida. Los Castros s/n, Santander, Spain
- ORCID: 0000-0003-2752-8086
- Email: rafael.granero@unican.es
**Stefano Scrobogna**- Affiliation: IMUS, University of Seville, 41012 Sevilla, Spain; and Basque Center of Applied Mathematics, Mazarredo 14, 48009, Bilbao, Spain
- MR Author ID: 1229361
- Email: sscrobogna@bcamath.org
- Received by editor(s): November 5, 2019
- Received by editor(s) in revised form: March 31, 2020
- Published electronically: September 18, 2020
- Additional Notes: The first author was funded by the grant MTM2017-89976-P from the Spanish government.

The research of the second author was supported by the Basque Government through the BERC 2018-2021 program and by the Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and “DESFLU” and by the European Research Council through the Starting Grant project H2020-EU.1.1.-639227 FLUID-INTERFACE - Communicated by: Catherine Sulem
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5181-5191 - MSC (2010): Primary 35Q35, 35R35, 35Q31, 35L25
- DOI: https://doi.org/10.1090/proc/15219
- MathSciNet review: 4163831