Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise

Fuente: arXiv
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Main Author: Goodair, Daniel
Format: Preprint
Published: 2024
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author Goodair, Daniel
author_facet Goodair, Daniel
contents We introduce an extended variational framework for nonlinear SPDEs with unbounded noise, defining three different solution types of increasing strength along with criteria to establish their existence. The three notions can be understood as probabilistically and analytically weak, probabilistically strong and analytically weak, as well as probabilistically and analytically strong. Our framework facilitates several well-posedness results for the Navier-Stokes Equation with transport noise, equipped with the no-slip and Navier boundary conditions.
format Preprint
id arxiv_https___arxiv_org_abs_2401_10076
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise
Goodair, Daniel
Analysis of PDEs
Probability
We introduce an extended variational framework for nonlinear SPDEs with unbounded noise, defining three different solution types of increasing strength along with criteria to establish their existence. The three notions can be understood as probabilistically and analytically weak, probabilistically strong and analytically weak, as well as probabilistically and analytically strong. Our framework facilitates several well-posedness results for the Navier-Stokes Equation with transport noise, equipped with the no-slip and Navier boundary conditions.
title Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise
topic Analysis of PDEs
Probability
url https://arxiv.org/abs/2401.10076