Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910416136830976 |
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| author | Khor, Calvin Miao, Changxing Su, Xiaoyan |
| author_facet | Khor, Calvin Miao, Changxing Su, Xiaoyan |
| contents | In this paper, we show that for $α\in(1/2,5/4)$, there exists a force $f$ and two distinct Leray-Hopf flows $u_1,u_2$ solving the forced fractional Navier-Stokes equation starting from rest. This shows that the J.L. Lions exponent is sharp in the class of Leray-Hopf solutions for the forced fractional Navier-Stokes equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_06358 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent Khor, Calvin Miao, Changxing Su, Xiaoyan Analysis of PDEs Primary 35F50, Secondary 35A02, 35Q35 In this paper, we show that for $α\in(1/2,5/4)$, there exists a force $f$ and two distinct Leray-Hopf flows $u_1,u_2$ solving the forced fractional Navier-Stokes equation starting from rest. This shows that the J.L. Lions exponent is sharp in the class of Leray-Hopf solutions for the forced fractional Navier-Stokes equation. |
| title | Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent |
| topic | Analysis of PDEs Primary 35F50, Secondary 35A02, 35Q35 |
| url | https://arxiv.org/abs/2306.06358 |