Liouville Type Theorem for Stationary Navier-Stokes Equations

Abstract

It is shown that any smooth solution to the stationary Navier-Stokes system in $R^3$ with the velocity field, belonging globally to $L_6$ and $BM{0}^{-1}$, must be zero.

7 pages

Cited by in corpus (30)

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• Decay and vanishing of some axially symmetric D-solutions of the Navier-Stokes equations
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• On Liouville-type theorems for the 2D stationary MHD equations
• On the Vanishing of some D-solutions to the Stationary Magnetohydrodynamics System
• Liouville type theorems for the stationary Hall-MHD equations in local Morrey spaces
• Asymptotic properties of generalized D-solutions to the stationary axially symmetric Navier-Stokes equations
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• Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second orderin unbounded domains
• Liouville theorem for steady-state solutions of simplified Ericksen-Leslie system
• Liouville theorem of axially symmetric Navier-Stokes equations with growing velocity at infinity
• On Liouville type theorem for a generalized stationary Navier-Stokes equations
• Remarks on Liouville type theorems for the 3D steady axially symmetric Navier-Stokes equations
• A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations
• On some Liouville type Theorems for the stationary MHD and Hall-MHD equations
• Refined Liouville-Type Theorems for the Stationary Navier--Stokes Equations
• Relative decay conditions on Liouville type theorem for the steady Navier-Stokes system
• Logarithmic improvement of a Liouville-type theorem for the stationary Navier--Stokes equations
• On Liouville type theorems in the stationary non-Newtonian fluids
• Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl
• A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang
• Liouville theorems for the Stokes equations with applications to large time estimates
• Conditional Liouville theorems for the Navier-Stokes equations
• An Lp-theory for fractional stationary Navier-Stokes equations
• On some Liouville type theorems for the stationary equations of MHD
• A note on optimal decay rates for the axisymmetric D-solutions to the steady Navier-Stokes equations
• Classification of solutions of the 2D steady Navier-Stokes equations with separated variables in cone-like domains