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Liouville theorems for the stationary Navier-Stokes equations under partial component conditions
We prove Liouville theorems for smooth stationary incompressible Navier-Stokes flows in $R^3$ with finite Dirichlet integral and velocity vanishing uniformly at infinity. If the partial components of velocity $(u_1,u_2)$ belong to $L^{4,\infty}$, then we show that $u$ must vanish. The second result
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