A variational approach to Navier-Stokes.

Ulisse Stefanelli (Università di Vienna)

I will discuss a variational approach to the incompressible Navier-Stokes system by means of stabilized Weighted-Inertia-Dissipation-Energy (WIDE) functionals. These are parameter-dependent functionals on entire trajectories whose minimization corresponds to an elliptic-in-time regularization of the system. By passing to the limit in the regularization parameter along subsequences of WIDE minimizers one recovers classical Leray-Hopf weak solutions. The tool can also be used as a variational selection principle in case boundary conditions are not imposed on some parts of boundaries, representing, e.g., outflows.
This is based on work in collaboration with Michal Bathory, Michael Ortiz, and Bernd Schmidt.