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arXiv · 2306.07857

Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces

Luigi Forcella·Oana Pocovnicu
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Abstract

We consider a fractional nonlinear wave equations (fNLW) with a general power-type nonlinearity, on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for a renormalized fNLW. We first construct the Gibbs measure associated with this equation by using the variational approach of Barashkov and Gubinelli. We then prove almost sure local well-posedness with respect to Gibbsian initial data, by exploiting the second order expansion. Finally, we extend solutions globally in time using Bourgain's invariant measure argument.

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Luigi Forcella, Oana Pocovnicu. 2023-06-13. Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces. https://arxiv.org/abs/2306.07857

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