Global small finite energy solutions for the incompressible magnetohydrodynamics equations in R+×R2

Abstract In this paper, we prove the global well-posedness for the incompressible magnetohydrodynamics (MHD) equations in the three-dimensional unbounded domain Ω : = R + × R 2 . More precisely, we construct global small Sobolev regularity solutions with the initial data near 0 for the three-dimensional MHD equations in Ω. The key point of the proof is to find the suitable initial approximation function such that the linearized equations around it admitted a partial dissipative structure when we carry out the weighted energy estimate. Meanwhile, the asymptotic expansion of Sobolev regularity solutions is given.