Topics in Hydrodynamics (Mathematics)

点击翻译按钮获取中文摘要

Dr. Friedlander's recent research involves the study of certain problems related to the equation of hydrodynamics (the Euler equations and the Navier-Strokes equations) and to the extended system of the equations of magnetohydrodynamics. The mathematics employed includes techniques from partial differential equations, asymptotic methods and dynamical systems. The problems studied are motivated by questions that arise in geophysical and astrophysical fluid dynamics. This research project will involve joint work with M.M. Vishik. Dr. Friedlander will continue her investigation of several facets of these problems. The research is described under four headings: (I)The "fast" dynamo problem; (II) Instability criteria for the Euler equations; (III) The existence of a complete system of Floquet root vectors in time periodic of fluid dynamics; (IV) Magnetohydrodynamic stability. Interactive activities at the host institution include: (1) teaching a graduate course on mathematical topics in fluid dynamics; (2) mentoring and counseling women students and postdocs in the mathematical sciences; and (3) organizing a two-day workshop of colloquium style lectures given by distinguished women mathematicians. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future significantly.