Random data Cauchy theory for supercritical wave equations II: a global existence result

• 成果类型: Article
• 署名作者: Burq, Nicolas; Tzvetkov, Nikolay
• 署名单位: Universite Paris Saclay; Institut Universitaire de France; Universite de Lille
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0123-0
• 发表日期: 2008
• 页码: 477-496
• 关键词: nonlinear schrodinger-equation; invariant-measures

摘要

We prove that the subquartic wave equation on the three dimensional ball Theta, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in boolean AND(s<1/2)(H-s(Theta) x Hs-1(Theta)). We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work [6] and invariant measure considerations, inspired by earlier works by Bourgain [2,3] on the non linear Schrodinger equation, which allow us to obtain also precise large time dynamical informations on our solutions.