This research is directed toward fluid dynamics and related areas of mathematics, including the theory of partial differential equations, dynamical systems theory and numerical analysis. The fluid.dynamical issues addressed include applications in astrophysics and geophysics, fundamental questions regarding the Navier.Stokes and Euler equations and numerical, analytical and asymptotic methods for their solution. The dynamical systems issues include the study of systems of ordinary differential equations drawn from fluid.dynamical problems, as well as the means of reducing partial differential equations to finite.dimensional form, both in the Hamiltonian and dissipative cases.
