Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Wednesday, December 18, 11:30 am – 12:30 pm

Zoom: 964 5417 6168, Passcode: dkumath

Title: Yudovich’s theory in the context of plasmas

Speaker: Haroune Houamed

Abstract: It is well known, due to Yudovich, that the two-dimensional Euler equations are globally well-posed for an initial vorticity that is solely bounded and integrable. Although justifying the sharpness of this result is still open, generally speaking, we tend to believe that Yudovich’s theory lies in the borderline between well-posedness and ill-posedness of the Euler equations. On the other hand, extending this theory to more general models, involving strong coupling with Euler’s vorticity, is more challenging and sometimes even fails to be true. In this talk, I will highlight a few aspects of positive and negative results in these directions before I move on to sketching the main ingredients behind the validity of Yudovich’s theory for the incompressible Euler—Maxwell system, which governs the evolution of an ideal plasma in a relativistic context. Moreover, it is to be emphasized that our approach allows us to analyze, in a rigorous way, the behavior of the global solutions within the non-relativistic regime, thereby deriving a classical MHD model from the Euler—Maxwell system.

Bio: Haroune holds a Ph.D. from the University of Côte d’Azur, France, where he defended his thesis in 2020. Since 2021, he has been a Postdoctoral Associate at New York University Abu Dhabi. His research focuses on Analysis and Nonlinear Partial Differential Equations (PDEs), particularly on models arising in incompressible fluid dynamics and plasmas. This encompasses questions on well-posedness, regularity, blow up, as well as the dynamical and asymptotic behavior of solutions to PDEs.