A generic existence theorem for convective motions in a viscous fluid

Summary Some years ago W.Velte 1]and A.Marino 2]have studied the problem of convective motions in a incompressible viscous fluid in dimensions two and three, respectively, focusing their interest in the case of nonuniqueness of the solution of the nonlinear system. They look at it as a bifurcation problem and prove the existence of solutions bifurcating from same line of trivial solutions under the hypothesis that the linearized operator has eigenvalues of odd multiplicities. They observe that the operators involved are not potential operators, thus variational tools can not be applied. In this paper, we prove that, in case of dimension two, for almost every domain , all the eigenvalues of the linearized operator are simple. Our procedure is related to that in 3];the fact that we deal with the system here, necessitates, however, some basic changes.Supported in part by C.N.R. (G.N.A.F.A.).