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
