**Title:** “Mathematical analysis of incompressible flow”

Prof. Milton C. Lopes Filho (UFRJ)

Description: This is na advanced course in PDE, which assumes a working knowledge of basic PDE at the level of L. C. Evans’ book.

Classes: Tuesdays and Fridays, 10:30-12:00, IMPA, Room 347.

Begins: March 11, 2014.

Syllabus:

- Derivation of the equations of Euler and Navier-Stokes;
- Symmetries and conserved quantities;
- Vorticity;
- Classical solutions, existence and uniqueness;
- Singularities, Beale-Kato-Majda;
- Weak solutions, vortex sheets, wild solutions;
- Boundary layers, Kato criterion;
- Turbulence;

References:

- A. Majda and A. Bertozzi – Vorticity and the Mathematical Theory of Incompressible Fluid Flow

- M. C. Lopes Filho, H. J. Nussenzveig Lopes and Y. Zheng - Weak solutions of the equations of incompressible and inviscid fluid dynamics