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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Well-posedness of water wave model with viscous effects
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by Rafael Granero-Belinchón and Stefano Scrobogna PDF
Proc. Amer. Math. Soc. 148 (2020), 5181-5191 Request permission


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.
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Additional 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:
  • 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:
  • 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:
  • MathSciNet review: 4163831