We consider the initial value problem for the Navier-Stokes equations modeling an incompressible fluid in three dimensions. It is well-known that this problem has a unique global-in-time mild solution for a suciently small initial condition u0 and for a small external force F in suitable scaling invariant spaces. We show that these global-in-time mild solutions are asymptotically stable under every (arbitrary large) L2-perturbation of their initial conditions.
The work is joint with Grsegorz Karch and Dominika Pilarczyk.