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.
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