ITALIANO

1)Spazi dell'idrodinamica
2)Il problema di Stokes: BVP e IBVP
3)L2-teoria di soluzioni regolari
4)esistenza globale per piccoli dati
5)criteri di regolarità e singolarità delle soluzioni
6)soluzioni deboli globali
7)teorema di struttura
8)questioni di unicità, regolarità e relazione dell'energia
9)congetture relative al problema mal posto

lecture notes

introduction to the understanding the analytic questions related to the Navier-Stokes equations

Laurea triennale in matematica

lezioni in aula

esame orale

1. Hydrodynamic spaces. Helmholtz decomposition Lq-Helmholtz ecomposition Some results concerning the Stokes operator
2. Regular solutions to problem Navier-Stokes equations
2.1 Galerkin method for PDE
2.2 Lq-theory (q≥2) for problemNavier-Stokes equations
2.3 Solutions with small initial data in Jn(Ω), n≥3
2.4 A remark on the question of the existence of regular solutions
3. L2-weak solutions.
3.1 Hopf weak solutions
3.2 Sufficient conditions for a weak solution in order to deduce regu-
larityproperties
3.3 Leray and Caffarelli-Kohn-Nirenberg weak solutions

Italian

1)Hydrodynamic spaces
2)The Stokes proble:the BVP and the IBVP
3)L2-theory for regular solutions
4)global existence for small data
5)some criterium of regularity and singularity of the solutions
6)weak solution as global solutions
7) structure theorem of a weak solution
8)uniqueness, regularity and energy equality open questions
9)congectures about ill posed problem

lecture notes

introduction to understanding the analytic questions related to the Navier-Stokes equations

Bachelor's degree in mathematics

lectures

oral exam

1. Hydrodynamic spaces. Helmholtz decomposition Lq-Helmholtz ecomposition Some results concerning the Stokes operator
2. Regular solutions to Navier-Stokes equations
2.1 Galerkin method for PDE
2.2 Lq-theory (q≥2) for Navier-Stokes equations
2.3 Solutions with small initial data in Jn(Ω), n≥3
2.4 A remark on the question of the existence of regular solutions
3. L2-weak solutions.
3.1 Hopf weak solutions
3.2 Sufficient conditions for a weak solution in order to deduce regu-
larityproperties
3.3 Leray and Caffarelli-Kohn-Nirenberg weak solutions