On the rigidity and existence of self-similar solutions to the Navier-Stokes Equations

Scale invariant or self-similar solutions, play important roles in the understanding of the regularity and asymptotic structures of the general solutions to the Navier-Stokes equations. In this talk, we talk about rigidity results and existence of large self-similar solutions to steady Navier-Stokes equations with arbitrary large external forces. We also talk about the existence of large two-dimensional forward self-similar solutions of the Navier-Stokes equations with generally non-integrable vorticity. These results require no smallness assumptions.