Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane
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| Format: | Preprint |
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2026
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| _version_ | 1866916066688499712 |
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| author | Chen, Shaoqing Sun, Yongzhong |
| author_facet | Chen, Shaoqing Sun, Yongzhong |
| contents | It has been conjectured that generic smooth solutions of the two-dimensional Euler equation exhibit linear growth of vorticity gradients. We prove an elementary arbitrary-background perturbation principle in the odd symmetric setting. More precisely, for any compactly supported nonnegative function in the half-plane, one can find an arbitrarily small smooth nonnegative perturbation whose associated solution undergoes linear-in-time filamentation in the quadrant. The main ingredients are the lower bound of the center of mass given by Iftimie-Sideris-Gamblin, and the velocity estimate for the sparse part to capture those slowly moving particles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_31541 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane Chen, Shaoqing Sun, Yongzhong Analysis of PDEs Primary 35Q35, Secondary 35Q31, 35B40, 35B65, 76B47 It has been conjectured that generic smooth solutions of the two-dimensional Euler equation exhibit linear growth of vorticity gradients. We prove an elementary arbitrary-background perturbation principle in the odd symmetric setting. More precisely, for any compactly supported nonnegative function in the half-plane, one can find an arbitrarily small smooth nonnegative perturbation whose associated solution undergoes linear-in-time filamentation in the quadrant. The main ingredients are the lower bound of the center of mass given by Iftimie-Sideris-Gamblin, and the velocity estimate for the sparse part to capture those slowly moving particles. |
| title | Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane |
| topic | Analysis of PDEs Primary 35Q35, Secondary 35Q31, 35B40, 35B65, 76B47 |
| url | https://arxiv.org/abs/2605.31541 |