On the existence of a stationary symmetric solution of the two- dimensional fluid flow problem (Q1896990)

For the problem \(\nu \Delta v - \nabla p = (v, \nabla) v + f, \quad \text{div} v = 0, \quad v |_{\partial \Omega} = a,\) considered in a bounded doubly connected domain \(\Omega \subset \mathbb{R}^2\), with a nonzero flux \[ \mu = \int_{S_j} (a,n) ds \quad (j = 1,2) \] of the field \(a\) through the components \(S_1\) and \(S_2\) of the boundary \(\partial \Omega = S_1 \cup S_2\), we establish the existence of a generalized solution under definite symmetry conditions for the domain \(\Omega\) and the fields \(a\) and \(f\).