A vorticity-based mixed formulation for the unsteady Brinkman-Forchheimer equations

In this work we propose and analyze an augmented mixed formulation for the time-dependent Brinkman-Forchheimer equations written in terms of vorticity, velocity and pressure.
The weak formulation is based on the introduction of suitable least squares terms arising from the incompressibility condition and the constitutive equation relating the vorticity and velocity. We establish existence and uniqueness of a solution to

Why general relativity does not admit enough observables

One of the biggest open problems in mathematical physics has been the problem of formulating a complete and consistent theory of quantum gravity. Some of the core technical and epistemological difficulties come from the fact that General Relativity is fundamentally a geometric theory and, as such, it ought to be invariant under change of coordinates by the arbitrary element of the diffeomorphism group Diff(M) of the ambient manifold M.