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A Class of Solutions for the Equations Governing the Steady Two‐Dimensional Motion of a Viscous Incompressible Liquid

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A general viscosity dependent solution for the stream function is found satisfying the simplest nondegenerate form of the steady flow Navier‐Stokes equations for a viscous incompressible liquid. The solution is two‐dimensional and is expressed in terms of arbitrary analytic functions in the fluid domain. This class of flows is generated by complex stream functions, and the region of definition is restricted by an inequality containing these analytic functions. A general potential flow, and degenerate Stokes or creeping flows are recovered as particular solutions in limiting cases.
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Document Type: Research Article

Affiliations: University of Toronto

Publication date: June 1, 1994

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