Thursday, June 6, 2024 - 12:00 in V2-210/216
Invariant Gibbs dynamics for fractional wave equations in negative Sobolev spaces
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Oana Pocovnicu from Heriot-Watt University
| Abstract: |
In this talk, we consider a fractional nonlinear wave equation with a
general power-type nonlinearity (FNLW) on the two-dimensional torus. Our
main goal is to construct invariant global-in-time Gibbs dynamics for
FNLW. We first construct the Gibbs measure associated with this
equation. By introducing a suitable renormalisation, we then prove
almost sure local well-posedness with respect to Gibbsian initial data.
Finally, we extend solutions globally in time by applying Bourgain's
invariant measure argument.
We also consider the case of initial data consisting of the
randomisation of a given pair of functions of negative regularities. We
show that, in this case, probabilistic well-posedness fails unless we
impose that the given pair has additional Fourier-Lebesgue regularity.
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