Math Courses

Applied Partial Differential Equation. Part I: Classical dynamics of incompressible fluids: the Euler and the Navier-Stokes equations

by Sara Daneri (GSSI)


Sara Daneri (GSSI)

The class will cover the following topics:

  • Derivation of the Euler and Navier-Stokes equations from conservation principles in the continuum hypothesis;
  • Conserved quantities and special solutions;
  • Local existence of solutions for regular initial data via energy methods;
  • Yudovich theorem on existence and uniqueness of two-dimensional solutions with bounded vorticity;
  • Leray-Hopf solutions of the Navier-Stokes equations;
  • Strong solutions and weak-strong uniqueness;
  • Serrin’s regularity result.