3 papers
math.AP2026
Rigorous analysis for the Dirac system on the quarter-plane
Hassan Babaei, Jerry L. Bona, Andreas Chatziafratis
Considered and analyzed below are fully non-homogeneous initial-boundary-value problems for the celebrated Dirac system, formulated on the spatial half-line. Analytical solution fo…
math.AP2026
Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence
Hassan Babaei, Mimi Dai
In turbulent flows, the Kolmogorov wavenumber characterizes the smallest scales at which viscous effects dominate. A mathematical analogue of this notion first introduced by Foias…
math.AP2025
Well-posedness of the electron MHD with partial resistivity
Mimi Dai, Hassan Babaei
Due to the singular nonlinear Hall term, the non-resistive electron magnetohydrodynamics (MHD) is not known to be locally well-posed in general. In this paper we consider the $2\fr…