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Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent
- Source :
- Bull. London Math. Soc., 55: 2705-2717 (2023)
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 14 pages; to appear in Bull. Lond. Math. Soc
- Subjects :
- Mathematics - Analysis of PDEs
Primary 35F50, Secondary 35A02, 35Q35
Subjects
Details
- Database :
- arXiv
- Journal :
- Bull. London Math. Soc., 55: 2705-2717 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2306.06358
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1112/blms.12889