Large Norm Inflation of the Current in the Viscous, Nonresistive Magnetohydrodynamics Equations
Abstract
Abstract. We consider the ideally conducting, viscous magnetohydrodynamics equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow and a constant magnetic field in a periodic infinite channel. In contrast to the Navier–Stokes equations this system is shown to exhibit algebraic instability and large norm inflation of the magnetic current on nonperturbative time scales.
Fields of Study & Subjects
Geophysics and Gravity Measurements
Geomagnetism and Paleomagnetism Studies
Solar and Space Plasma Dynamics
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 2
- Pages
- 1699–1743
- Publication date
- 10 April 2026
- Language
- EN