Anomalous Regularization in Kraichnan's Passive Scalar Model

2024/07/23 by Galeati, Lucio, Grotto, Francesco, Maurelli, Mario · 4 citations
#35R36 #76F25 #76F55 #76M35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.16668

Abstract

We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and Hölder regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity.

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