Frequency decay for Navier-Stokes stationary solutions

TL;DR

This paper proves exponential frequency decay of stationary Navier-Stokes solutions in three dimensions, with enhanced decay under small external forces and damping, aligning with turbulence theory predictions.

Contribution

It establishes exponential frequency decay for stationary Navier-Stokes solutions, including pointwise decay under small forces and with damping, advancing understanding of solution regularity.

Findings

Exponential frequency decay for solutions with regular external force

Pointwise exponential decay under small external force

Decay results improved with added damping term

Abstract

We consider stationary Navier-Stokes equations in R 3 with a regular external force and we prove exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions according to the K41 theory. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.