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L-2-Critical Nonuniqueness for the 2D Navier-Stokes Equations

机译：L-2-Critical Nonuniqueness for the 2D Navier-Stokes Equations

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In this paper, we consider the 2D incompressible Navier-Stokes equations on the torus. It is well known that for any L-2 divergence-free initial data, there exists a global smooth solution that is unique in the class of CtL2 weak solutions. We show that such uniqueness would fail in the class CtLp if p < 2. The non-unique solutions we constructed are almost L-2-critical in the sense that (i) they are uniformly continuous in L-p for every p < 2; (i i) the kinetic energy agrees with any given smooth positive profile except on a set of arbitrarily small measure in time.

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