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Anomalous Regularization in Kraichnan's Passive Scalar Model

Probability 2024-07-24 v1 Analysis of PDEs

Abstract

We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\"older 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.

Keywords

Cite

@article{arxiv.2407.16668,
  title  = {Anomalous Regularization in Kraichnan's Passive Scalar Model},
  author = {Lucio Galeati and Francesco Grotto and Mario Maurelli},
  journal= {arXiv preprint arXiv:2407.16668},
  year   = {2024}
}

Comments

24 pages

R2 v1 2026-06-28T17:51:11.601Z