Abstract. We study the large time behavior of solutions of the second grade fluid system in the space R 2 . Using scaled variables and introducing several functionals in weighted Sobolev spaces, we prove that the solution of the second grade fluid equations converges to the Oseen vortex, if the initial data are small enough. We also give an estimate of the rate of convergence.

In this work, we consider the flow of a second grade fluid in a conducting domain of R 3 and in the presence of a magnetic field. When the initial data are of arbitrary size, we prove that the solution of the magnetohydrodynamics problem exists for a small time and is unique. We also show the global existence of solutions for small initial data.where J is the current density, and E and B are the electric field and the magnetic induction satisfying the Maxwell's equations curlB D J,(2)Eliminating J and E between (1) and (2), we find that the magnetic field B satisfies the following equation Á