PDE Aspects of the Navier-Stokes Equations

In this lecture we will discuss mathematical aspects of the NavierStokes equations. We will recall some of the important open problems and mention a few recent results. Consider a ball of radius R moving in an incompressible fluid of constant density ρ at constant velocity U . We expect that a force F is needed to keep the ball in motion (to overcome the “resistance of the medium”). The force is usually called the drag force. What is the formula for the drag force? This classical problem of Fluid Mechanics was considered already by Newton, who derived the formula