Showing math.APShow all
3 papers · 1 filter
math.AP2026
Equilibria for the Vlasov-Maxwell system related to plasma confinement
Justin Holmer, Katherine Zhiyuan Zhang
By working in a setting of azimuthal and -directional invariance, we reduce the existence of electrically neutral, magnetically driven, equilibria of the two-species Vlasov-Maxw…
math.AP2025★ 11 cited
Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1
We prove that near-threshold negative energy solutions to the 2D cubic (-critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof cons…
math.AP2024
Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
Xuwen Chen, Justin Holmer
We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We constru…