On the Ohm–Navier–Stokes system in magnetohydrodynamics

We study a mathematical structure of the Ohm–Navier–Stokes system that describes the incompressible dissipative evolution of a plasma. We apply the nonlinear semigroup theory and construct a unique regular solution which satisfies the system at least locally-in-time. We show that, for small initial data, this solution solves the system globally-in-time. We also introduce another scheme to construct solutions for less regular initial data.