We consider the density properties of divergence-free vector
fields b∈L1([0,1],\BV([0,1]2)) which are ergodic/weakly
mixing/strongly mixing: this means that their Regular Lagrangian
Flow Xt is an ergodic/weakly mixing/strongly mixing measure...
The incompressible porous media (IPM) equation describes the
evolution of density transported by an incompressible velocity
field given by Darcy’s law. Here the velocity field is related to
the density via a singular integral operator, which is...
I will discuss the construction of continuous solutions to
the incompressible Euler equations that exhibit local dissipation
of energy and the surrounding motivations. A significant open
question, which represents a strong form of the Onsager...
I will describe a new geometric approach for the shock formation
problem for the Euler equations. A complete description of
the solution along the hypersurface of first singularities or
preshocks will be given.
The quadratic Monge optimal transportation problem can be
revisited in Euler's language of Hydrodynamics as was explained by
Jean-David Benamou and the speaker about 20 years ago. It turns out
that Einstein's theory of gravitation, at least in...
