Anomalous Regularization in Kraichnan's Passive Scalar Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910539100192768 |
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| author | Galeati, Lucio Grotto, Francesco Maurelli, Mario |
| author_facet | Galeati, Lucio Grotto, Francesco Maurelli, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomalous Regularization in Kraichnan's Passive Scalar Model Galeati, Lucio Grotto, Francesco Maurelli, Mario Probability Analysis of PDEs 76F55, 76M35, 76F25, 35R36 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. |
| title | Anomalous Regularization in Kraichnan's Passive Scalar Model |
| topic | Probability Analysis of PDEs 76F55, 76M35, 76F25, 35R36 |
| url | https://arxiv.org/abs/2407.16668 |