Asymptotic decay of solutions to 3D MHD equations

In the very recent work Wang and Wang (2014) proved that the initial value problem for the three dimension incompressible MHD equations has a global solutions (u,B)∈C([0,∞);χ−1)(u,B)∈C([0,∞);χ−1), provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients. In this paper, we prove that global solutions u,Bu,B that was obtained in Wang and Wang (2014) is asymptotic to zero in sense of the norm of the space χ−1χ−1 as time goes to infinity. Moreover, stability of global solutions is also discussed.