On Fluid Mechanics and its Difficulties
On Fluid Mechanics and its Difficulties

Andrei Tarfulea , Princeton University
Fine Hall 314
I'll spend the first half (but hopefully less) of the talk giving an abridged introduction to the Euler and NavierStokes equations, covering the basic derivations and some of the known results. Afterwards, I will provide two examples to illustrate some of the difficulties in analyzing these equations. The first example is a 1dimensional model problem for the 3dimensional Euler equations that mimics turbulent behavior. This model is simpler, but fails global wellposedness in a bad way. The second example is an EulerianLagrangian recasting of NavierStokes that fails global wellposedness for somewhat topological reasons.