Existence of axisymmetric solutions of the stationary system of Navier-Stokes equations in a class of domains with noncompact boundary (Q1070119)

The existence of an axisymmetric solution of the Navier-Stokes equation for a noncompact domain \(O\) (obtained rotating a two-dimensional domain \(D\) which have two exits to infinity) is proved. Using a sequence of expanding bounded domains which at the limit exhaust the domain \(D\), one obtains a sequence of functions which converges weakly in Sobolev space \(W^ 1_ 2(O')\) to the solution of the problem, for every bounded subdomain \(O'\subset O\). The uniqueness is established using an additional condition at infinity.