The theorem of fast growth of a small magnetic field (``Dynamo'') for magnetic hydrodynamics equations with pulsing initial velocities (Q1385856)

The author considers the equations of an incompressible plasma \[ {\partial u\over \partial t} +\langle u,\nabla \rangle u=- \nabla P-{1\over 4\pi} (H\times \text{rot} H)+ \text{Re}^{-1} \Delta u+F(x,t, \text{Re}^{-1}), \] \[ {\partial H\over \partial t}=\text{rot} (u \times H) +\text{Re}^{-1}_M \Delta H,\quad \text{div} u=0, \quad \text{div} H=0, \quad \text{Re}_M \geq\text{Re}\gg 1 \] and presents results concerning the existence and the behavior of solutions if the Reynolds number \(\text{Re} \to\infty\).