MATHEMATICAL PHYSICS II
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2020/2021
- Teacher
- ARIANNA PASSERINI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- MAT/07
Training objectives
- Aim of the course is a review, as deep as possible, of the mathematical methods in fluid mechanics, from the dynamical symmetries algebra to functional analysis theorems, simply through the study of their applications to that only physical phenomenon consisting in the heat transport by convective fluxes. The discussion of Bénard's convection in 2D starts from the Eulerian approach to continuum dynamics, then, through the derivation of the Newtonian stress tensor, the non dimensional parameters involved in the conservation laws, and the Boussinesq approximation, one gets a writing with insight of the system of PDE, where the border of the applications is known as well as the physical phenomena it is demanding to describe. At the end, the tools to prove existence and stability (even optimal) of the solutions are given
At the end of the course, the student will have acquired, on one hand, notions and tecniques in the modeling of continuum media, and on the other hand, he will have gained experience in the application of abstract methods in Functional Analysis and Calculus of Variations to mechanically motivated (especially non-linear) problems. Prerequisites
- In order to fruitfully attend the course, the student should have notions in the following areas (in addition to the first-two-years undergraduate teachings):
Continuum Mechanics (only basic/general notions are needed)
Functional Analysis (Banach-, Hilbert-, Sobolev spaces; however more or less extensive recalls will be made during the course when necessary) Course programme
- Review of Continuum Mechanics, balance laws, Boussinesq approximation, the Bénard problem in 2D, existence and linear stability, optimal non linear stability
Didactic methods
- The lectures are in streaming
Learning assessment procedures
- The final exam consists in an oral discussion on the subjects of the course
Reference texts
- Lecture notes. References on each topics will be given while lecturing
