Mathematical Sciences: Variational Methods and Applications

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8901477 Auchmuty The principal investigator will conduct research on the construction and analysis of variational principles for certain problems that are important in applications. He will develop, and implement, some new algorithms for numerically solving these variational problems. The problems to be studied include non-self-adjoint elliptic eigenproblems and their application to linear hydrodynamic stability theory, and nonlinear eigenvalue problems for the Hartree and Hartree-Fock equations which arise in quantum theory. Another class of problems centers on the variational characterization of solutions of the Navier-Stokes equations, including the properties and consequences of these principles. The numerical research will center on numerical methods for finding eigenvalues and eigenvectors of both symmetric and non-symmetric matrices, also the numerical simulation of the equilibria of rotating self-gravitating fluids, which are simple hydrodynamical models of stars and planets.