Mathematical hydrodynamics
| 1 & 2. 2D and 3D Navier-Stokes (NS) equations
Leray theory: weak and strong solutions for 3D NS, weak-strong uniqueness, local in time theory, 2D NS |
| 3. Euler equation in 2D
Strong solutions and the Wolibner theorem, weak solutions and the Yudovich theorem |
| 4. Euler equation in 3D and the inviscous limit |
| 5 & 6. Around the Onsager conjecture
The conjecture, the work of Duchon-Robert, weak solutions of Euler equation of non-constantenergy. |
| 7. Appendix (if time permits): the great open problems
of mathematical
hydrodynamics. |
| PREREQUISITES: weak and strong solutions of nonlinear PDE, Sobolev spaces and the embedding theorems. The knowledge of these topics is sufficient (say) if it allows to read first sections of Chapter 1 of the book J-L Lions "Quelques methodes de resolution des problems aux limites non lineares". |