Speaker
Peter Topalov, Northeastern University
Abstract
We show that the Navier-Stokes equation for a viscous incompressible fluid in \mathbb{R}^d is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as |x|\to\infty of any a priori given order. The solution depends analytically on the initial data and time so that for any 0<\vartheta<\pi/2 it can be holomorphically extended in time to a conic sector in \mathbb{C} with angle 2\vartheta at zero. I will also discuss the approximation of solutions by their asymptotic parts.