Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909985995227136 |
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| author | Bagnara, Marco Galeati, Lucio |
| author_facet | Bagnara, Marco Galeati, Lucio |
| contents | We prove strong well-posedness results for the stochastic 2D Euler equations in vorticity form and generalized SQG equations, with $L^p$ initial data and driven by a spatially rough, incompressible transport noise of Kraichnan type. Previous works addressed this problem with noise of spatial regularity $α\in (0,1/2)$, in a setting where a rougher noise yields a stronger regularization. We remove this limitation by allowing any $α\in (0,1)$, covering the same range of parameters for which anomalous regularization effects are known to occur in passive scalars. In particular, this covers the physically relevant case $α=2/3$, associated with the Richardson-Kolmogorov scaling of energy cascade. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise Bagnara, Marco Galeati, Lucio Probability Analysis of PDEs 60H50, 60H15, 35Q35, 76M35 We prove strong well-posedness results for the stochastic 2D Euler equations in vorticity form and generalized SQG equations, with $L^p$ initial data and driven by a spatially rough, incompressible transport noise of Kraichnan type. Previous works addressed this problem with noise of spatial regularity $α\in (0,1/2)$, in a setting where a rougher noise yields a stronger regularization. We remove this limitation by allowing any $α\in (0,1)$, covering the same range of parameters for which anomalous regularization effects are known to occur in passive scalars. In particular, this covers the physically relevant case $α=2/3$, associated with the Richardson-Kolmogorov scaling of energy cascade. |
| title | Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise |
| topic | Probability Analysis of PDEs 60H50, 60H15, 35Q35, 76M35 |
| url | https://arxiv.org/abs/2601.05982 |