Mathematical Sciences: Variational Methods and Applications

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The investigator proposes to develop and analyze variational principles for various problems that arise in mechanics and in chemical systems theory. He also proposes to develop algorithms and numerical methods for approximating the solutions of these problems. Particular attention will be devoted to the variational characterization of the solutions of the Navier-Stokes equations, the initial value problem for pipe flow and of various problems in hydrodynamic stability. It is also planned to study certain second order equations including equations from mechanics and certain wave equations and various eigenvalue problems. Variational methods of the type proposed here have numerous applications in computational methods in engineering and other sciences.