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Almost global wellposedness of the 2-D full water wave problem

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Abstract

We consider the problem of global in time existence and uniqueness of solutions of the 2-D infinite depth full water wave equation. It is known that this equation has a solution for a time period [0,T/ε] for initial data of the form ε Ψ, where T depends only on Ψ. In this paper, we show that for such data there exists a unique solution for a time period [0,e T/ε]. This is achieved by better understandings of the nature of the nonlinearity of the full water wave equation.

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  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Sijue Wu

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  1. Sijue Wu
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Correspondence to Sijue Wu.

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Financial support provided in part by NSF grant DMS-0400643.

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Wu, S. Almost global wellposedness of the 2-D full water wave problem. Invent. math. 177, 45–135 (2009). https://doi.org/10.1007/s00222-009-0176-8

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  • DOI: https://doi.org/10.1007/s00222-009-0176-8

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