Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs

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 extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence.
format Preprint
id arxiv_https___arxiv_org_abs_2408_11678
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs
Goodair, Daniel
Analysis of PDEs
Probability
We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence.
title Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs
topic Analysis of PDEs
Probability
url https://arxiv.org/abs/2408.11678