Topics in Hydrodynamics (Mathematics)

Friedlander博士最近的研究涉及与流体动力学方程（欧拉方程和Navier-Strokes方程）和磁流体动力学方程的扩展系统有关的某些问题的研究。所使用的数学包括偏微分方程、渐近方法和动力系统的技术。所研究的问题是由地球物理和天体物理流体动力学中出现的问题引起的。这个研究项目将涉及与M.M. Vishik的联合工作。弗里德兰德博士将继续研究这些问题的几个方面。这项研究分为四个标题：(I)“快速”发电机问题；（II） Euler方程的不稳定性判据；（III）流体动力学时间周期中Floquet根向量的完备系统的存在性；（四）磁流体动力稳定性。在主办机构的互动活动包括：(1)教授一门关于流体动力学数学主题的研究生课程；(2)对数学科学领域的女学生、女博士后进行指导和辅导；(3)组织由杰出女数学家举办的为期两天的研讨会式讲座。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。通过鼓励妇女参与科学，这是对国家未来的重大投资。

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.