Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus - Université de Versailles Saint-Quentin-en-Yvelines
Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2024

Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus

Résumé

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 I-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.
Fichier principal
Vignette du fichier
global-dynamics-for-the-stochastic-nonlinear-beam-equations-on-the-four-dimensional-torus.pdf (771.92 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04836034 , version 1 (20-12-2024)

Licence

Identifiants

Citer

Andreia Chapouto, Guopeng Li, Ruoyuan Liu. Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2024, ⟨10.1017/prm.2024.87⟩. ⟨hal-04836034⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

More