Mathematical Sciences: Variational Methods and Applications

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9302318 Auchmuty The investigator studies the construction, analysis and numerical simulation of variational principles for certain problems in fluid mechanics, field theories, chemistry and astronomy. He also studies certain minimax problems and the development of algorithms for the numerical solution of nonconvex extremal problems. The problems to be studied here include the analysis and development of algorithms for modeling atoms and molecules using the equations of quantum chemistry. Similar methods also apply in studying the equations for vortices in fluids (which are important in studying hurricanes and tornadoes) and models of rotating stars and planets. These are all described by systems of nonlinear partial differential equations which arise from "nonconvex" variational principles. This proposal studies aspects of the mathematics of such problems and also questions of developing algorithms for solving these problems computationally. ***