Nonlinear energy stability of magnetohydrodynamics Couette and Hartmann shear flows: A contradiction and a conjecture

Here we study the nonlinear stability of magnetohydrodynamics plane Couette and Hartmann shear flows. We prove that the streamwise perturbations are stable for any Reynolds number. This result is in a contradiction with the numerical solutions of the Euler–Lagrange equations for a maximum energy problem. We solve this contradiction with a conjecture. Then, we rigorous prove that the least stabilizing perturbations, in the energy norm, are the...