Research on this project is directed toward the application of analysis and computation to mathematical modeling problems in fluid dynamics. Specific problems under study are drawn from magnetohydrodynamics as well as the dynamics of incompressible fluids. A general and unified variational approach will be employed to address a variety of questions concerning the existence, regularity and stability of both magnetostatic equilibria and steady vortex flows having one spatial symmetry. These questions involve nonlinear elliptic eigenvalue problems formulated from basic physical principles as optimization problems with many nonlinear constraints. New iterative methods for solving this class of variational problems will be developed, and their convergence properties will be examined analytically. Similar methods will be adapted to improve numerical solvers for the governing evolution equations by a nonlinear projection technique. The investigations also address certain nonlinear wave motions in fluids, especially internal waves in density- stratified fluids and inertial waves in swirling flows. The goal of the research is to enhance the theoretical aspects of fluid dynamics by studying the relevant nonlinear partial differential equations. ***
