Global well-posedness and large-time behavior of solutions to the 3D inviscid magneto-micropolar equations with damping

Abstract

We first establish the existence of global strong solutions to the 3D inviscid incompressible magneto-micropolar equations with a velocity damping in Sobolev spaces , where the norm of initial data is small, but its higher order derivatives could be large. Combining the norm or norm of the initial magnetic field is finite with some tricky interpolation estimates, we show and two faster decay rates for the velocity and the micro-rotation field , which are shown to be the usual type of the optimal time decay rates for 3D inviscid incompressible magneto-micropolar equations with damping. We then conclude the damping term contributes to weaken the assumption of initial condition and enhance the decay rate of velocity compared to the classical incompressible viscous magneto-micropolar equations. Meanwhile, for the 3D inviscid compressible magneto-micropolar fluid, the damping term also has the same effect on the decay rate of the velocity.