Changxing Miao

Forward self-similar solutions of the Navier-Stokes equations in R^n

We investigate forward self-similar solutions to the incompressible Navier--Stokes equations with homogeneous initial data $u_0(x)=\sigma(x/|x|)/|x|$, $x\in\mathbb R^n$, focusing on the critical four-dimensional case. For the existence theory in dimensions $3\leq n\leq5$, we develop a Galerkin scheme for the Leray prof...