Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 266, Issue 4, Pages 2319-2340Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2013.06.002
Keywords
Gibbs measure evolution; Nonlinearities
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Funding
- NSF [DMS-0808042, DMS-0835373]
- Fernholz Foundation
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We establish new global well-posedness results along Gibbs measure evolution for the nonlinear wave equation posed on the unit ball in R-3 via two distinct approaches. The first approach invokes the method established in the works Bourgain (1994, 1996) [3-5] based on a contraction-mapping principle and applies to a certain range of nonlinearities. The second approach allows to cover the full range of nonlinearities admissible to treatment by Gibbs measure, working instead with a delicate analysis of convergence properties of solutions. The method of the second approach is quite general, and we shall give applications to the nonlinear Schrodinger equation on the unit ball in subsequent works Bourgain and Bulut (2013) [10,11]. (C) 2013 Published by Elsevier Inc.
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