On Steady Ideal Flows with Nonvanishing Vorticity in Cylindrical Domains

University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

Abstract: A paper by Alber shows the existence of steady, inviscid incompressible flows with nonvanishing vorticity for general three-dimensional domains with smooth boundary. In this thesis we show the existence of such flows in cylindrical domains under the conditions that there is no flow through the side of the cylinder, nonzero flow into the cylinder at all points in the bottom, and nonzero flow out of the cylinder at all points in the top. The flow is constructed by adding a perturbation with nonvanishing vorticity to an already existing flow with no vorticity. To show that this indeed gives us another flow we use a fixed point argument. This can be done if we put certain restrictions on the boundary conditions that define the vorticity of the perturbation.

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