Seminars & Colloquia Calendar
Global existence of Navier-Stokes equations for non-decaying initial data
Tai-Peng Tsai, University of British Columbia
Location: Hill 705
Date & time: Tuesday, 09 April 2019 at 1:40PM - 3:00PM
Abstract: Consider the Cauchy problem of incompressible Navier-Stokes equations in R^3 with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a time-global weak solution has been known.
However, such data do not include constants, and the only known global solutions for non-decaying data are either for perturbations of constants, or when the velocity gradients are in Lp with finite p. In this talk, I will outline how to construct global weak solutions, first for non-decaying initial data whose local oscillations decay, no matter how slowly, second for initial data whose uniform local square integral grows in scale under a certain rate.
These are joint work with Kwon and Bradshaw, respectively.