Large-time behaviour of solutions to the magneto-hydrodynamics equations (Q1914726)

We establish lower and upper bounds for the rate of decay of the total energy and of the magnetic energy of solutions to the magnetohydrodynamics equations on \(\mathbb{R}^n\), \(2\leq n\leq 4\). It is shown that weak solutions subject to large initial data outside a class of functions with total radially equidistributed energy decay algebraically (rather than exponentially). It is also proved that initial data with radially equidistributed energy gives rise to weak solutions which decay exponentially (rather than algebraically).