Vorticity confinement for 2D incompressible flows in an infinite cylinder
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866911515518435328 |
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| author | Buttà, Paolo Cavallaro, Guido |
| author_facet | Buttà, Paolo Cavallaro, Guido |
| contents | We study the confinement of vorticity for two-dimensional incompressible flows in an infinite cylinder. For Navier-Stokes solutions with non-negative and compactly supported initial vorticity, we derive quantitative decay estimates showing that the vorticity mass outside regions whose distance from the initial support grows like $\sqrt{t\log^αt}$ (with $α>1$) or like $t^β$ (with $β>1/2$) becomes, respectively, super-polynomially or stretched-exponentially small. The analysis combines an iterative scheme with an antisymmetry property of the Biot-Savart kernel. In the Euler case, by coupling this approach with a first-moment estimate from [Commun. Math. Phys., 367, 1077-1093, 2019], we recover the confinement bound of [Commun. Math. Phys., 367, 1077-1093, 2019] and refine it slightly: the diameter of the vorticity support grows at most like $(t\log t)^{1/3}$, rather than $t^{1/3}\log^2 t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vorticity confinement for 2D incompressible flows in an infinite cylinder Buttà, Paolo Cavallaro, Guido Analysis of PDEs Mathematical Physics 76D17, 76B47, 37N10 We study the confinement of vorticity for two-dimensional incompressible flows in an infinite cylinder. For Navier-Stokes solutions with non-negative and compactly supported initial vorticity, we derive quantitative decay estimates showing that the vorticity mass outside regions whose distance from the initial support grows like $\sqrt{t\log^αt}$ (with $α>1$) or like $t^β$ (with $β>1/2$) becomes, respectively, super-polynomially or stretched-exponentially small. The analysis combines an iterative scheme with an antisymmetry property of the Biot-Savart kernel. In the Euler case, by coupling this approach with a first-moment estimate from [Commun. Math. Phys., 367, 1077-1093, 2019], we recover the confinement bound of [Commun. Math. Phys., 367, 1077-1093, 2019] and refine it slightly: the diameter of the vorticity support grows at most like $(t\log t)^{1/3}$, rather than $t^{1/3}\log^2 t$. |
| title | Vorticity confinement for 2D incompressible flows in an infinite cylinder |
| topic | Analysis of PDEs Mathematical Physics 76D17, 76B47, 37N10 |
| url | https://arxiv.org/abs/2603.13926 |