Global well-posedness holds for logarithmically hyperdissipative 3D Navier-Stokes with high-mode Lie-transport noise via probabilistic effective dissipation from a scaling limit.
Delayed Blow-up in 3D Fluids via Pseudo-transport Noise
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abstract
We establish scaling limit results for fluid dynamics equations driven by pseudo-transport noise. The behaviour of noise at small scales is governed by a parameter a. This extends previous results by Flandoli and Luo (2020) and Galeati (2020), which correspond to a=0 in our setting. Depending on the value of a, we prove that the noise delays the potential blow-up of both the 3D Euler and Navier-Stokes (NS) equations with high probability.
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Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations
Global well-posedness holds for logarithmically hyperdissipative 3D Navier-Stokes with high-mode Lie-transport noise via probabilistic effective dissipation from a scaling limit.