Unsteady equipartition MHD solutions

The unsteady equipartition solutions are introduced that describe a plasma relaxation in regime of a strong interaction between the plasma velocity V and the magnetic field B and depend on all four variables t,x,y,z. The solutions exist when the kinematic viscosity ν is equal to the magnetic diffusivity η and V=±B/√(ρμ). The exact equipartition solutions to the boundary value problem with the ''no-slip'' boundary condition are derived. The solutions depend on infinitely many parameters and describe the plasma relaxation in a ball with a constant pressure at the boundary. The translationally invariant exact solutions are obtained for ν≠η for which plasma is confined in cylindrical domains by the magnetic field B only while the plasma pressure P is zero at the boundary and is positive inside the domains