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Well-posedness of a model for water waves with viscosity

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Title: Well-posedness of a model for water waves with viscosity
Author(s): Ambrose, David; Bona, Jerry; Nicholls, David
Abstract: The water wave equations of ideal free–surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well–posedness theory. In consequence of both theoretical and computational difficulties with the full water wave equations, various asymptotic approximations have been proposed, analyzed and used in practical situations. In this essay, we establish the well–posedness of a model system of water wave equations which is inspired by recent work of Dias, Dyachenko, and Zakharov (Phys. Lett. A, 372:2008). The model in question includes dissipative effects and is weakly nonlinear. The present contribution is a first step in a larger program centered around the Dias-Dychenko-Zhakharov system.
Issue Date: 2012-06
Publisher: American Institute of Mathematical Sciences
Citation Info: Ambrose, D. M., Bona, J. L., & Nicholls, D. P. 2012. Well-Posedness of A Model for Water Waves with Viscosity. Discrete and Continuous Dynamical Systems-Series B, 17(4): 1113-1137. DOI: 10.3934/dcdsb.2012.17.1113
Type: Article
Description: © 2012 by American Institute of Mathematical Sciences, Discrete and Continuous Dynamical Systems - Series B DOI: 10.3934/dcdsb.2012.17.1113
URI: http://hdl.handle.net/10027/8452
ISSN: 1531-3492
Sponsor: DMA gratefully acknowledges support from the National Science Foundation through grants DMS-0926378, DMS-1008387, and DMS-1016267. JLB thanks the University of Illinois at Chicago and the Universit´e de Paris Val de Marne for support during this collaboration. DPN gratefully acknowledges support from the National Science Foundation through grant No. DMS–0810958, and the Department of Energy under Award No. DE–SC0001549.
Date Available in INDIGO: 2012-08-14
 

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