Title: Partial Differential Equations and Applied Mathematics Seminar (2016.7.29)

Author: CMAC

Date: 2016-07-26 (14:49)

Date/Time: July 29th, Fri., 2:00 ~ 3:00 PM

Location: Science Building #262 Yonsei University

Speaker: Dr. Shangkun Weng

Affiliation: 포스텍 수학과

Title: Decay properties of axially symmetric D-solutions to the steady Navier-Stokes equations

Abstract:

In this talk, we investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The new achievements are two folds. One is improved decay rates of $u_{\theta}$ and $\nabla {\bf u}$, especially we show that $|u_{\theta}(r,z)|\leq c\left(\frac{\log r}{r}\right)^{\frac{1}{2}}$ for any smooth axially symmetric D-solutions to the Navier-Stokes equations. Another is the first decay rate estimates in the $Oz$-direction for smooth axially symmetric flows without swirl. We do not need any small assumptions on the forcing term.