On the hydrostatic approximation of Navier-Stokes-Maxwell system with Gevrey data

In this paper, we prove the local well-posedness of a scaled anisotropic Navier-Stokes-Maxwell system in a 2-D striped domain with initial data around some nonzero background magnetic field in Gevrey-2 class. Then we rigorously justify the limit from the scaled anisotropic equations to the associated hydrostatic system and provide with the precise convergence rate. Finally, with small initial data in Gevrey-$\frac{3}{2}$ class, we also extend the lifespan of thus obtained solutions to a longer time interval.