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

by Sara Daneri (GSSI)

Friday 1 Nov 2019, 09:00 → Saturday 30 Nov 2019, 11:00 Europe/Rome

Lecturer:
Sara Daneri (GSSI)

Description:
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.