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.