Global Existence for Capillary Water Waves. Issue 4 (14th August 2014)

• Record Type: Journal Article
• Authors: Germain, Pierre; Masmoudi, Nader; Shatah, Jalal
• Is Part Of: Communications on pure and applied mathematics. Volume 68:Issue 4(2015:Apr.)
• Page Start: 625
• Page End: 687
• Publication Date: 2014-08-14
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21535
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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. © 2015 Wiley Periodicals, Inc.</p> </abstract>