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The Bardos-Tartar Conjecture for the Navier-Stokes Equations
We consider the incompressible viscous Navier-Stokes equations in dimension $d=2,3$ with periodic boundary conditions and time-independent external forcing. When $d=2$, the Bardos-Tartar conjecture asks whether the set of solutions at any given positive time is dense in the Hilbert subspace of $L^2$
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