Recent progress on ideal incompressible plasma models

par Haroune Houamed (NYU Abu-Dhabi)

mardi 24 janv. 2023, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

The behavior of plasmas, or electrically conducting fluids, is often well-described by a set of hydrodynamic equations coupled with Maxwell’s equations, through the action of an electromagnetic force. Many aspects of the analysis of such models are met with important challenges due to the hyperbolic nature of Maxwell’s system. 

 

In this talk, I will focus on the two dimensional Euler–Maxwell equations, which describes the evolution of ideal plasmas. I will explain how to extend Yudovich’s method to construct global and unique solutions to that model by shielding the light on several key arguments and considerations that permit the obtainment of a uniform global bound with respect to the speed of light $c \in (0,\infty)$. That matter of fact allows us to study the regime $c \to \infty$ and to derive (particular) MHD system, as well.

 

In the second part of my talk, I will begin with a quick review of several recent methods that are utilized to study the strong convergence of perturbation of Euler’s equations in the Yudovich class of solutions. Then, I will present our new proof, which hangs upon an abstract ''extrapolation'' argument, and I will show how to apply it to study the asymptotic regime $c\rightarrow \infty$ in the Euler--Maxwell equations.

 

The results of my talk are based on a joint work with Diogo Arsenio from NYUAD.