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On the local well-posedness for a full-dispersion Boussinesq system with surface tension


Authors: Henrik Kalisch and Didier Pilod
Journal: Proc. Amer. Math. Soc. 147 (2019), 2545-2559
MSC (2010): Primary 35Q53, 35A01, 76B15; Secondary 35E05, 35E15
DOI: https://doi.org/10.1090/proc/14397
Published electronically: February 14, 2019
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Abstract: In this note, we prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions. Those systems can be seen as a weak nonlocal dispersive perturbation of the shallow-water system. Our method of proof relies on energy estimates and a compactness argument. However, due to the lack of symmetry of the nonlinear part, those traditional methods have to be supplemented with the use of a modified energy in order to close the a priori estimates.


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Additional Information

Henrik Kalisch
Affiliation: Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
Email: Henrik.Kalisch@uib.no

Didier Pilod
Affiliation: Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
Email: Didier.Pilod@uib.no

DOI: https://doi.org/10.1090/proc/14397
Received by editor(s): May 22, 2018
Received by editor(s) in revised form: August 30, 2018
Published electronically: February 14, 2019
Additional Notes: This research was supported by the Bergen Research Foundation (BFS), the Research Council of Norway, and the University of Bergen.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society