Home>Events>Seminars

Lr-Helmholtz-Weyl decomposition in 3D exterior domains (IV) Proof of the $L^r$-Helmholtz-Weyl decomposition in 3D exterior domains (V) Application to the stationary Navier-Stokes equations

2021-12-24 14:00-15:30 ZOOM

Abstract:In this series of talks, the Helmholtz-Weyl decomposition in three dimensional exterior domains is established within the Lr-setting for 1 <r<∞.  In an exterior domain having compact boundary with finite many disjoint smooth closed surfaces,we show the existence of weak solutions of the stationary Navier–Stokes equations in 3D. The outline is

1.Overview of Lr-Helmholtz-Weyl decomposition in 3D exterior domains 
2.$L^r$-harmonic vector field in 3D exterior domains
3.$L^r$-variational inequality for scalar and vector potentials in 3D exterior domains
4.Proof of the $L^r$-Helmholtz-Weyl decomposition in 3D exterior domains
5.Application to the stationary Navier-Stokes equations

Zoom:
https://zoom.us/j/85437391848?pwd=eHVLUVFGMEhDaGZVS3BIU3ZtMnc5dz09

ID:854 3739 1848
Passwords:918572