Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus
Abstract
We study global-in-time dynamics of the stochastic nonlinear beam equations (SNLB) with an additive space-time white noise, posed on the four-dimensional torus. The roughness of the noise leads us to introducing a time-dependent renormalization, after which we show that SNLB is pathwise locally well-posed in all subcritical and most of the critical regimes. For the (renormalized) defocusing cubic SNLB, we establish pathwise global well-posedness below the energy space, by adapting a hybrid argument of Gubinelli- Koch-Oh-Tolomeo (2022) that combines the -method with a Gronwall-type argument. Lastly, we show almost sure global well-posedness and invariance of the Gibbs measure for the stochastic damped nonlinear beam equations in the defocusing case.
Keywords
Cite
@article{arxiv.2312.13901,
title = {Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus},
author = {Andreia Chapouto and Guopeng Li and Ruoyuan Liu},
journal= {arXiv preprint arXiv:2312.13901},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2005.10570 by other authors