Seminar Analysis and Mathematical Physics: Umberto Pappalettera (Universität Bielefeld)

On anomalous regularity in Kraichnan’s model of turbulent transport

In this talk I will present a new “anomalous regularisation” result for solutions of the stochastic transport equation \partial_t \rho + \circ \partial_t W \cdot \nabla \rho = 0, where W is a Gaussian, homogeneous, isotropic noise with \alpha-H\”older space regularity and compressibility ratio \wp < \frac{d}{4\alpha^2}. The proof is obtained by studying the local behaviour around the origin of solutions to a degenerate parabolic PDE in non-divergence form, which is of independent interest. Based on joint work with Theodore Drivas and Lucio Galeati.
 

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