Nontrivial stationary solutions of the 2D Navier-Stokes equations exist on the torus at regularity L^{2-epsilon} cap dot H^{-epsilon} for every epsilon in (0,1).
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Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces
Nontrivial stationary solutions of the 2D Navier-Stokes equations exist on the torus at regularity L^{2-epsilon} cap dot H^{-epsilon} for every epsilon in (0,1).