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<p>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.</p>

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Anomalous regularization in kraichnan’s passive scalar model

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Lucio Galeati,
  • Francesco Grotto,
  • Mario Maurelli

摘要

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.