Existence of three-dimensional, steady, inviscid, incompressible flows with nonvanishing vorticity (Q1204139)

The author studies the flow of an inviscid incompressible medium through a bounded, simply connected domain of \(\mathbb{R}^ 3\). He is particularly interested in constructing solutions with nonvanishing vorticity. In general the expectation is that these type of flows are unstable and this instability introduces difficulties into the existence proof. The author proves that if there exists a solution of a particular boundary value problem with sufficiently small vorticity, then there exists a neighbourhood of this solution and flows with nonvanishing vorticity in this neighbourhood with special stability properties.