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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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On partial regularity for stochastic 3D Navier-Stokes equations Sapienza University of Rome, Italy It is known that global weak solutions to the stochastic 3D Navier-Stokes equations with various types of multiplicative noise exist. Capturing their regularity is one of the most fundamental open problems in fluid dynamics, even in the absence of noise. The set of singularities can be of a very intricate nature, even of fractal type. Partial regularity aims to provide sharp estimates on the fractal dimension (e.g., Hausdorff) for such sets. In this talk, we will discuss a way to estimate the set of singular times, that is, times at which a weak solution is not regular. In particular, we extend to the stochastic setting the well-known 1/2-bound on the fractal dimension of singular times, which goes back to the works by Leray and Scheffer. Interestingly, the bound is independent of the roughness of the noise. Our viewpoint is new even in the deterministic case, and can be applied to a wide class of stochastic PDEs, e.g., reaction-diffusion equations. | |
