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

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arxiv 2408.11678 v1 pith:TO23G7YI submitted 2024-08-21 math.AP math.PR

Daniel Goodair This is my paper · ORCID
classification math.APmath.PR
keywords blow-upsolutionsexistencecriterionframeworkimprovedmaximalspdes
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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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Cited by 1 Pith paper

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  1. Closed Estimates of Leray Projected Transport Noise and Strong Solutions of the Stochastic Euler Equations

    math.AP 2025-07 conditional novelty 8.0 of 10

    Closed Sobolev estimates for Leray-projected transport noise yield unique local strong solutions of the 3D stochastic Euler equations, with blow-up characterized by L1([0,T]; W^{1,∞}).

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