Any Ḣ¹ solution to the stationary Navier-Stokes equations in R³ is identically zero when its radial velocity component lies in L^p(R³) for 3/2 < p ≤ 3.
Seregin , A Liouville type theorem for steady-state Navier-Stokes equations
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Stationary Navier-Stokes solutions in R^3 are trivial under L^{9/2 + ε(·)} integrability with ε(·)>0, including versions that only constrain behavior at infinity.
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Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component
Any Ḣ¹ solution to the stationary Navier-Stokes equations in R³ is identically zero when its radial velocity component lies in L^p(R³) for 3/2 < p ≤ 3.
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Liouville Theorems Above the Critical $9/2$ Threshold for Stationary Navier-Stokes Equations
Stationary Navier-Stokes solutions in R^3 are trivial under L^{9/2 + ε(·)} integrability with ε(·)>0, including versions that only constrain behavior at infinity.