A remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions (Q340990)

The purpose of this paper is to study a stationary Navier-Stokes equation NEWLINE\[NEWLINE\begin{cases} -\Delta v+(v\cdot \nabla)v+\nabla p=0, \\ \operatorname{div} v=0 \end{cases}NEWLINE\]NEWLINE in \(\mathbb{R}^3\). The main theorem states that for a certain asymptotic estimate for \(x\), the finite Dirichlet integral \(D(v)<\infty\).NEWLINENEWLINEThe proofs use generalized Hölder inequality, Calderon-Zygmund kernel, Biot-Savart law, Liouville theorem for harmonic functions, Riesz transform, Marcinkiewicz interpolation theorem.