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1. Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent

Author

Khor, Calvin, Miao, Changxing, and Su, Xiaoyan

Subjects
Mathematics - Analysis of PDEs, Primary 35F50, Secondary 35A02, 35Q35
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., Comment: 14 pages; to appear in Bull. Lond. Math. Soc

Published
2023
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