Abstract
This paper describes variational methods for finding the stationary velocity fields of given vorticity which obey either no-flux or no-slip boundary conditions. The density of the fluid is assumed to be known, continuous and bounded away from zero and the domain is bounded, connected and has a C 1,1 boundary. Necessary conditions on the vorticity for there to be velocity fields with finite kinetic energy are derived. The existence of velocity fields is then proven subject to these necessary conditions and the vorticity being 6/5th power integrable on the region. This is done by using variational principles for the solutions. These principles are suitable for numerical simulation and computation. Some continuous dependence results are described.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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