Global cauchy problem of 2D generalized MHD equations

Amann, H.: Maximal regularity for nonautonoumous evolution equations. Adv. Nonlinear Stud. 4, 417–430 (2004)

Córdoba, A., Córdoba, D.: A maximum principle applied to quasi-geostrophic equations. Comm. Math. Phys. 249, 511–528 (2004)

Fan, J., Nakamura, G., Zhou, Y.: Global well-posedness of 2D MHD equations with fractional diffusion, preprint (2012)

Ji, E.: On two-dimensional magnetohydrodynamic equations with fractional diffusion. Nonlinear Anal. 80, 55–65 (2013)

Kato, T., Ponce, G.: Comutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41, 891–907 (1988)

Lemarié-Rieusset, P.G.: Recent Developments in the Navier-Stokes Problem. Chapman & Hall/CRC, Boca Raton (2002)

Mattingly, J.C., Sinai, Ya G.: An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations. Commun. Contemp. Math. 1, 497–516 (1999)

Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinues. Ann. Inst. Fourier (Grenoble) 15, 189–258 (1965)

Tran, C.V., Yu, X., Zhai, Z.: On global regularity of 2D generalized magnetohydrodynamic equations. J. Differ. Equ. 254(10), 4194–4216 (2013)