A sharp form of Nevanlinna's second main theorem of several complex variables.
We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.
This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field B, respectively the local deformation gradient F, satisfies for 1/p + 1/q = 1 and 2 < p ≤ ∞, then the corresponding local solution can be extended beyond time T.
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