Nonuniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes Equations in three dimensions, up to the J. L. Lions exponent
Abstract
In this paper, we show that for α∈(1/2,5/4), there exists a force f and two distinct Leray-Hopf flows u1,u2 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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