On the convergence to the Navier-Stokes-Maxwell system with solenoidal Ohm's law

The incompressible Navier-Stokes-Maxwell system with solenoidal Ohm’s law can be viewed as as the asymptotic limit of the two-fluid incompressible Navier-Stokes-Maxwell system as the momentum transfer coefficient tends to zero (see [1], Arsénio, Ibrahim and Masmoudi, Arch. Ration. Mech. Anal., 2015). We prove this limit rigorously without loss of regularity by using the idea of frequency envelope.