activity
20242026
collaborators

5 papers

math.AP2026

Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD

Yuan Cai

We address the plasma-vacuum interface problem in the two dimensional space. The plasma region is governed by the ideal incompressible magnetohydrodynamic equations. The vacuum reg…

math.AP2026

Global nonlinear stability of the 2D incompressible viscous non-resistive MHD under sheared magnetic field

Yuan Cai, Bin Han, Na Zhao

We study the two-dimensional incompressible viscous non-resistive magnetohydrodynamics in the periodic strip , subject to a smooth sheared background magn…

math.AP2025

Small Alfvén Number Limit for the Global-in-time Solutions of Incompressible MHD Equations with General Initial Data

Yuan Cai, Xiufang Cui, Fei Jiang +1

The small Alfvén number (denoted by ) limit (one type of large parameter limits, i.e. singular limits) in magnetohydrodynamic (abbr. MHD) equations was first proposed…

math.AP2024

Global current-vortex sheets in the two-dimensional ideal incompressible MHD

Yuan Cai, Zhen Lei

The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of cu…

math.AP2024

Large data global existence for coupled massive-massless wave-type systems

Yuan Cai, Shijie Dong, Kuijie Li +1

We consider 3D Klein-Gordon-Zakharov (KGZ) and Dirac-Klein-Gordon (DKG) systems, where a common feature is that there exist both massless and massive fields in each system. We esta…