# Mathematical Sciences Research Institute

Home » Euler/Navier Stokes (Part 2): Global-in-time regularity of the Navier-Stokes equations with hyper-dissipation

# Seminar

Euler/Navier Stokes (Part 2): Global-in-time regularity of the Navier-Stokes equations with hyper-dissipation March 18, 2021 (09:30 AM PDT - 10:30 AM PDT)
Parent Program: Mathematical problems in fluid dynamics MSRI: Online/Virtual
Speaker(s) Liaosha Xu (University of Virginia)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Video
Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:  Further results are developed for showing the critical nature of the Navier-Stokes equation.  It is proved that global-in-time smooth solutions exist for the Navier-Stokes equations with hyper-dissipation, i. e. the equations $\partial_t u+(-\Delta)^\beta u+ u\cdot\nabla u+\nabla p=0 , \quad \textrm{div}\ u=0, \qquad \beta >1$ with the hypothesis that there is only one singular point at a possible blow-up time.