Invariant measure for the cubic wave equation on the unit ball of R³

This paper deals with the invariance of a measure on Sobolev spaces of low regularity under the flow of the cubic non linear wave equation on the unit ball of R³ under the assumption of spherical symmetry. It presents two aspects, an analytic one which includes the treatment of local properties of the flow, and a probabilistic one, which is mainly related to the global extension of the flow and the invariance of the measure.

Keywords

invariant measure, wave equation, spherical symmetry

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 76-xx.

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Published 23 June 2011