Global Existence for Capillary Water Waves
- 14 August 2014
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 68 (4) , 625-687
Abstract
Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space‐time resonance method and commuting vector fields.Keywords
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Funding Information
- National Science Foundation (DMS-1101269)
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