25 February – Buyang Li : A bounded numerical solution with a small mesh size implies existence of a smooth solution to the time-dependent Navier–Stokes equations

Buyang Li: Thursday 25 February at 14:00

We prove that for a given smooth initial value, if one finite element solution of the three-dimensional time-dependent Navier–Stokes equations is bounded by $M$ when some sufficiently small step size $\tau < \tau _M$ and mesh size $h < h_M$ are used, then the true solution of the Navier–Stokes equations with this given initial value must be smooth and unique, and is successfully approximated by the numerical solution.