Stability of singular solutions to the Navier-Stokes system

Marco Cannone, Grzegorz Karch, Dominika Pilarczyk, Gang Wu

Published 2020-12-23Version 1

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.