On the linear stability problem for Jeffery-Hamel flows

We study the linear stability of a family of Jeffery-Hamel solutions which satisfy a zero flux condition. With a suitable regularization of these velocity profiles we show that the linearized perturbation equation is well-posed on a weighted L² space with a certain class of radial weights, in the example of a half plane or in the whole plane. We prove that the perturbed Stokes operator of this system is the generator of a strongly continuous analytic semigroup. We also describe some formal asymptotics under which the linear stability problem could be reduced to a one dimensional problem for which we state a formal perturbation theory.