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2017 On the 3-dimensional water waves system above a flat bottom
Xuecheng Wang
Anal. PDE 10(4): 893-928 (2017). DOI: 10.2140/apde.2017.10.893

Abstract

As a starting point for studying the long-time behavior of the 3-dimensional water waves system in the flat bottom setting, we try to improve the understanding of the Dirichlet–Neumann operator in this set-up. As an application, we study the 3-dimensional gravity waves system and derive a new energy estimate of L2L type, which has good structure in the L-type space. This has been used in our Ph.D. thesis (2016) to prove the global regularity of the 3-dimensional gravity waves system for suitably small initial data.

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Xuecheng Wang. "On the 3-dimensional water waves system above a flat bottom." Anal. PDE 10 (4) 893 - 928, 2017. https://doi.org/10.2140/apde.2017.10.893

Information

Received: 18 February 2016; Revised: 16 January 2017; Accepted: 25 February 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1367.35130
MathSciNet: MR3649370
Digital Object Identifier: 10.2140/apde.2017.10.893

Subjects:
Primary: 35Q35, 76B15

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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