Mathematics > Probability
arXiv:2606.15425 (math)
[Submitted on 13 Jun 2026]
Abstract:We study well-posedness of stochastic parabolic equations with gradient nonlinearities. Our analysis is based on recent maximal-regularity frameworks for nonlinear stochastic parabolic equations in critical spaces. We extend the existing results by controlling drift and noise coefficient separately. This way we can allow for less regular driving noise in case of subcritical dispersion coefficients. Our approach, based on gluings of local solutions, moreover implies new continuation criteria. We then apply our existence result and the continuation criteria to show global well-posedness of phase-field models of moving boundary problems.
Submission history
From: Amjad Saef [view email]
[v1]
Sat, 13 Jun 2026 18:26:44 UTC (575 KB)
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