In the paper “Space analyticity and bounds for derivatives of solutions to the evolutionary equations of diffusive magnetohydrodynamics”, V. Zheligovsky has given solutions to the three following mutually related problems:

– to carry over the known a priori bounds for arbitrary-order space derivatives of solutions to the Navier–Stokes equation to space-periodic solutions to the equations of diffusive magnetohydrodynamics;

– to derive similar a priori bounds for arbitrary-order space derivatives of the first-order time derivative of the Fourier–Galerkin approximants of the MHD solutions and to prove that the bounds are admitted by weak solutions to the equations of magnetohydrodynamics;

– to reveal a link between these bounds and space analyticity of the MHD solutions at almost all times.

More*“Space analyticity and integral bounds for solutions to equations of magnetohydrodynamics”*