Wellposedness and Asymptotic behavior for a two-dimensional Incompressible Euler–Maxwell system

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Haroune Houamed (New York University Abu Dhabi)

Abstract: We prove the existence and uniqueness of Yudovich-type solutions to the Euler equations for a two-dimensional incompressible fluid coupled with the full set of Maxwell’s equations for electromagnetism. This is shown to hold under the condition that the speed of light is sufficiently large (compared to the velocity of the plasma, loosely speaking). Moreover, due to a refined analysis of the dispersive (–dissipative) properties of Maxwell’s equations, involving suitable high–low–frequency cutoff (in terms of the speed of light), the bounds on the solution are shown to be uniform with respect to the speed of light. This matter of fact allows us to derive (a simple version of) the MHD system as the speed of light tends to infinity. In our setting, the convergence of the solution in strong topologies comes with a rate and it relies on a robust stability mechanism of perturbations of the Euler equations in Yudovich’s class combined with a fine study of the behavior (evanescence) of the electric field in the non-relativistic regime. This is based on joint work with Diogo Arsenio from NYUAD.