Anne Nouri

On the Milne Problem and the Hydrodynamic Limit for a Steady Boltzmann Equation Model

For a stationary nonlinear Boltzmann equation in a slab with a particular truncation in the collision operator, the Milne problem for the boundary layer together with a weak type of hydrodynamic behavior in the interior of the slab are studied by nonperturbative methods in the small-mean-free-path limit.

Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution

A finite Larmor radius approximation is rigourously derived from the Vlasov equation, in the limit of large (and uniform) external magnetic field. Existence and uniqueness of a solution is proven in the stationary frame.We study a finite Larmor radius model used to describe the ions distributions in the core of a toka-mak plasma, that consist in a gyro-kinetic transport equation, coupled with an electro-neutrality equation. Since the last equation do not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. Next we study the two-dimensional dynamics in the direction perpendicular to the magnetic field and prove thanks to the smoothing effects of the collisions and of the gyro-average the global existence of solutions, as well as short time uniqueness and stability.

A Vlasov equation with Dirac potential used in fusion plasmas

Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This pathology appears on the full nonlinear problem, well-posed locally in time with analytic initial data, but generally ill-posed in the Hadamard sense. Eventually with a very different class of solutions, mono-kinetic, which constrains the structure of the density distribution, the problem becomes locally in time well-posed.

Boltzmann Asymptotics with Diffuse Reflection Boundary Conditions.

StrongL1-convergence towards a stationary solution when time tends to infinity is established for the solutions of the time-dependent nonlinear Boltzmann equation in a bounded domain Ω ⊂ ℝ3 with constant temperature on the boundary. The collisionless case is first investigated in the varying temperature case.

A large data existence result for the stationary Boltzmann equation in a cylindrical geometry

AnL1-existence theorem is proved for the nonlinear stationary Boltzmann equation with hard forces and no small velocity truncation—only the Grad angular cut-off-in a setting between two coaxial rotating cylinders when the indata are given on the cylinders.

Macroscopic models for ionization in the presence of strong electric fields

Abstract Starting from a kinetic model for electrons in a weakly ionized plasma, a spherical harmonic expansion (SHE-) model is derived by a formal asymptotic analysis for strongly disparate masses of electrons and ions. The macroscopic limit of the SHE-model for high fields gives a high field extension of standard macroscopic models for ionization.

An existence result for a quantum BGK model

A class of kinetic BGK models for Bose-Einstein statistics are considered for the stationary frame in a slab. Existence of bounded measure solutions is proven for Planckian diffuse boundary conditions with a given total inflow. Compactness properties are extracted from the L^1 part of the generalized Planckian distribution function and the boundary behavior.

Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability.

An Euler-Poisson system in plasmas

A local existence and uniqueness result is proved for the three-dimensional Euler-Poisson system without a pressure term which arises in plasma physics.

A global existence and uniqueness theorem for a model problem in dynamic elasto-plasticity with isotropic strain-hardening

We prove the global existence and uniqueness of the weak solution to the initial boundary value problem for an elastic-plastic solid with isotropic strain-hardening on a bounded domain in three space dimensions.