APDEs Seminar

In this talk, I will discuss several regularity criteria that provide geometric constraints on the possible finite-time blowup of solutions of the Navier-Stokes equation. This approach, based on the strain formulation of the Navier-Stokes regularity problem, not only gives geometric criteria for blowup in terms of the eigenvalues of the strain matrix, but also improves previous geometric regularity criteria involving the vorticity. Finally, I will discuss finite-time blowup for a model equation for the self-amplification of strain that respects these geometric constraints.