# Bienvenue - Laboratoire Jacques-Louis Lions

## Partenariats

| lire cette page en
Internships (10th and 11th grades high school students)
Job shadowing (Year 10, Year 11 students) See https://www.math.univ-paris-diderot.fr/diffusion/index

### Key figures

#### 189 people work at LJLL

##### 86 permanent staff

80 researchers and permanent lecturers

6 engineers, technicians and administrative staff

##### 103 non-permanent staff

74 Phd students

15 post-doc and ATER

14 emeritus scholars and external collaborators

January 2022

### A voir

#### Stability and interaction with walls for magnetic fusion plasmas

##### Upcoming seminars (See events in the agenda)

Tuesday 21 January 2021 at 11am : Claude Bardos (Université de Paris)

##### Summary

The object of this talk is to report on a joint ongoing program with Nicolas Besse Prof. Observatoire de la Cote d’Azur et Université de Nice.

The quasi linear approximation for solutions of the Vlasov equation is a very popular tool in Plasma Physic cf. [1] which proposes, for the quantity :
q ( ∫f (x, v, t)dx) , (1)
the solution of a parabolic, linear or non linear evolution equation
∂_t q(t, v) − ∇_v (D(q, t ; v)∇_v q) = 0 . (2)

Since the Vlasov equation is a hamiltonian reversible dynamic while (2) is not reversible whenever D(q, t, v) ≠ 0 the problem is subtle. Hence I will do the following things :

1. Give some sufficient conditions, in particular in relation with Landau damping that will imply that D(q, t, v) ≃ 0 .

2. Building on contributions of [3] and coworkers show the validity of the approximation (2) for large time and for a family of convenient randomized solutions.

3. In the spirit of a Chapman Enskog approximation formalize the very classical physicist approach for a short time approximation under analyticity assumptions.

References

[1] Plasma Physic in the 20th century as told by players. Guest editors.:P. Diamond, U. Frisch and Y. Pomeau. Vol 43 , 4-5, December 2018.

[2] N.A. Krall, A.W. Trivelpiece Principles of plasma physics, McGraw-Hill, 1973.

[3] F. Poupaud, A. Vasseur, Classical and quantum transport in random media, J. Math. Pures Appl. 82 711–748 (2003).

#### Location

Seminar room 15-16, 3rd floor, room 309

Laboratoire Jacques Louis Lions

Sorbonne Université

4 place jussieu, 75252 Paris FRANCE

You can get easy access to the place with the lift of tower 16, situated on the left when arriving on the campus.map