The effect of viscous coefficients on the lifespan of 3-D anisotropic magnetohydrodynamic system

In this paper, the authors investigate some lower bound estimates of the lifespan of magnetohydrodynamic equations with full dissipation and that of anisotropic magnetohydrodynamic equations. They first obtain the lower bound of the lifespan to magnetohydrodynamic equations when the viscosity coefficients $ \nu_1,\nu_2,\nu_3 $ and the magnetic diffusion coefficients $ \mu_1,\mu_2,\mu_3 $ are all positive. Then, they also establish the lower bound of the lifespan when some of them vanish. The lower bounds of the lifespan show that the effect of the influence on these lower bound estimates associated with these weights of $ \mu_1,\mu_2,\mu_3 $ and $ \nu_1,\nu_2,\nu_3 $ are different. These results help to understand the nonlinear structure of the magnetohydrodynamic system more comprehensively.