Stability of singular solutions to the Navier-Stokes system

TL;DR

This paper develops mathematical methods to analyze the asymptotic behavior of solutions to the 3D Navier-Stokes equations, including singular solutions caused by singular external forces, in both spatial and temporal limits.

Contribution

It introduces new techniques for studying the asymptotics of singular solutions to the Navier-Stokes system with singular external forces.

Findings

Asymptotic properties for large space variables

Asymptotic properties for large time values

Analysis of solutions with singular external forces

Abstract

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem or with the stationary problem where solutions may be singular due to singular external forces which are either singular finite measures or more general tempered distributions with bounded Fourier transforms. We present results on asymptotic properties of such solutions either for large values of the space variables (so called the far-field asymptotics) or for large values of time.