Global solutions to 3-D Navier–Stokes–Maxwell system slowly varying in one direction

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Gaocheng YueAbstractThe present paper is devoted to the well-posedness issue of solutions of a full system of the 3-D incompressible magnetohydrodynamic (MHD) equations with large initial velocity and magnetic field slowly varying in one space variable. By means of the anisotropic Littlewood–Paley analysis we prove the global well-posedness of solutions in the framework of anisotropic type Besov spaces for ϵ and σ sufficiently small. Toward this and due to the divergence-free property of magnetic field, the proof is based on unified energy estimates which is valid for the magnetic field satisfying the inhomogeneous damped wave equation.

Source: Nonlinear Analysis: Real World Applications - November 29, 2019 Category: Research Source Type: research