an:06965740
Zbl 1404.35374
Ye, Zhuan; Zhao, Xiaopeng
Global well-posedness of the generalized magnetohydrodynamic equations
EN
Z. Angew. Math. Phys. 69, No. 5, Paper No. 126, 26 p. (2018).
00418238
2018
j
35Q35 35B65 76W05 35R11
generalized MHD equations; global regularity; long time decay; Fourier-Herz spaces
Summary: In this paper, we establish the global existence of mild solutions to the \(n\)-dimensional generalized MHD system provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients and the fractional powers. In addition, we also establish the existence of the global small solution in the Fourier-Herz spaces. Finally, we prove the long time decay of the global solutions in the corresponding spaces.