Refined Liouville-Type Theorems for the Stationary Navier--Stokes Equations

Abstract

We study smooth solutions to the three-dimensional stationary Navier--Stokes equations and establish new Liouville-type theorems under refined decay assumptions. Building on the work of Cho et al., we introduce a refinement to previously known integrability criteria and analyze the associated averaged quantities. Our main result shows that if the $L^p$ growth rate of a solution remains bounded for some $3/2 < p < 3$, then the solution must be trivial. The proof combines averaged decay estimates, energy inequalities, and an iteration scheme.