Invariant measure for a three dimensional nonlinear wave equation

Details Invariant measure for a three dimensional nonlinear wave equation Invariant measure for a three dimensional nonlinear wave equation

2007-07-10

arxiv.org/abs/0707.1445v1

Mathematics

Analysis of PDEs

Scientific paper

We study the long time behavior of the subcritical (subcubic) defocussing
nonlinear wave equation on the three dimensional ball, for random data of low
regularity. We prove that for a large set of radial initial data in
$\cap_{s<1/2} H^s(B(0,1))$ the equation is (globally in time) well posed and we
construct an invariant measure.

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