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Daily Overview |
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Sto1: Stochastic analysis and differential equations Location: L602 Session Chair: Alexandra Blessing | |
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Global Solutions for Stochastically Controlled Fluid Dynamics Models 1: Babes-Bolyai University, Romania; 2: Imperial College London We introduce a carefully constructed stochastic perturbation whose diffusion coefficient grows super-linearly with the solution norm. The noise is designed to act selectively, becoming effective as the norm approaches potential blow-up, while its quadratic variation generates a stabilizing second-order mechanism. Under suitable structural assumptions on the drift term, we show that the resulting SPDE admits global strong solutions almost surely across three levels of initial regularity. In particular, the stochastic control prevents finite-time blow-up and extends the lifespan of solutions to all times, including regimes where global deterministic well-posedness remains open. This is joint work with Dan Crisan, based on the paper: Lang, O., Crisan, D. Global solutions for stochastically controlled fluid dynamics models. Stoch PDE: Anal Comp (2025). | |
