Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914664228585472 |
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| author | Ambrose, David M. Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig |
| author_facet | Ambrose, David M. Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig |
| contents | We consider the three-dimensional Navier-Stokes equations, with initial data having second derivatives in the space of pseudomeasures. Solutions of this system with such data have been shown to exist previously by Cannone and Karch. As the Navier-Stokes equations are a parabolic system, the solutions gain regularity at positive times. We demonstrate an improved gain of regularity at positive times as compared to that demonstrated by Cannone and Karch. We further demonstrate that the solutions are analytic at all positive times, with lower bounds given for the radius of analyticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus Ambrose, David M. Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig Analysis of PDEs 76D05 35B65 35K45 76D03 We consider the three-dimensional Navier-Stokes equations, with initial data having second derivatives in the space of pseudomeasures. Solutions of this system with such data have been shown to exist previously by Cannone and Karch. As the Navier-Stokes equations are a parabolic system, the solutions gain regularity at positive times. We demonstrate an improved gain of regularity at positive times as compared to that demonstrated by Cannone and Karch. We further demonstrate that the solutions are analytic at all positive times, with lower bounds given for the radius of analyticity. |
| title | Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus |
| topic | Analysis of PDEs 76D05 35B65 35K45 76D03 |
| url | https://arxiv.org/abs/2402.01038 |