An elementary proof of the global existence and uniqueness theorem to 2-D incompressible non-resistive MHD system

Abstract

In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and non-resistive MHD system under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^{\infty }$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.

15 pages. arXiv admin note: substantial text overlap with arXiv:1403.1085

References in corpus (2)

• Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity
• Global small solutions to 2-D incompressible MHD system

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