Global existence and decay estimate of solutions to magneto-micropolar fluid equations

Abstract

We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in R3. Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the H3 norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms H˙−s(0≤s<32) or homogeneous Besov norms B˙2,∞−s(0<s≤32), we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual Lp−L2(1≤p≤2) type of the decay rates without requiring that the Lp norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in R2 with large initial data.