Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent
| Autor: | Khor, Calvin, Miao, Changxing, Su, Xiaoyan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bull. London Math. Soc., 55: 2705-2717 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms.12889 |
| Popis: | In this paper, we show that for $\alpha\in(1/2,5/4)$, 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. Comment: 14 pages; to appear in Bull. Lond. Math. Soc |
| Databáze: | arXiv |
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