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arXiv · 2408.11678

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

Daniel Goodair
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Abstract

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.

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Daniel Goodair. 2024-08-21. Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs. https://arxiv.org/abs/2408.11678

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