ATTRACTING CURVES ON FAMILIES OF STATIONARY SOLUTIONS IN 2-DIMENSIONAL NAVIER-STOKES AND REDUCED MAGNETOHYDRODYNAMICS

Families of stable stationary solutions of the two-dimensional incompr essible homogeneous Euler and ideal reduced magnetohydrodynamic equati ons are shown to be attracting for the corresponding viscous perturbat ions of these systems, i.e. for the Navier-Stokes and the reduced visc ous MHD equations with magnetic diffusion. Each solution curve of the dissipative system starting in a cone around the family of stationary solutions of the unperturbed conservative system defines a shadowing c urve which attracts the dissipative solution in an exponential manner. As a consequence, the specific exponential decay rates are also deter mined. The techniques to analyse these two equations can be applied to other dissipative perturbations of Hamiltonian systems. The method in its general setting is also presented.