On scale-invariant solutions of the Navier-Stokes equations

14 June 2013
12:00
Vladimir Sverak
Abstract

The optimal function spaces for the local-in-time well-posedness theory of the Navier-Stokes equations are closely related to the scaling symmetry of the equations. This might appear to be tied to particular methods used in the proofs, but in this talk we will raise the possibility that the equations are actually ill-posed for finite-energy initial data just at the borderline of some of the most benign scale-invariant spaces. This is related to debates about the adequacy of the Leray-Hopf weak solutions for predicting the time evolution of the system. (Joint work with Hao Jia.)

  • OxPDE Special Seminar