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arXiv · 2306.06358

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

Calvin Khor·Changxing Miao·Xiaoyan Su
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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.

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Calvin Khor, Changxing Miao, Xiaoyan Su. 2023-06-10. Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent. https://doi.org/10.1112/blms.12889

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