Fluid Flows at Large

流体流动在大的建议研究摘要。Schonbek这个项目是继续对流体力学的三个基本方程进行分析。这些是Navier-Stokes和磁流体动力学（MHD）方程和二维准地转（2dQG）气象方程。对于Navier-Stokes方程，我们的努力将集中在分析半空间或可能的圆锥区域上的自相似解。兴趣将是他们的规律性和明确描述的解决方案。对于MHD方程，研究将集中在耗散仅依赖于速度时解的渐近行为。对于地转方程，研究将集中在描述绕障碍物流动的长时间行为。 Navier-Stokes方程的分析是理解流体流动的基础。任何明确的解决方案都有助于描述哪些可能的流动可以持续。当人们加上磁场的影响，并假设流体中含有带电粒子和离子时，MHD方程就产生了。本计画将探讨在无磁耗散的情形下，这些方程式的解。QG方程的分析是一个障碍物周围气流的模型，这是气象学中的一个常见问题。

Fluid Flows at Large Abstract of Proposed ResearchMaria E. Schonbek This project is to continue work on the analysis of three fundamental equations that are basic for fluid mechanics. These are the Navier-Stokes and Magneto-hydrodynamic (MHD) equations of hydrodynamics and the 2d quasi-geostrophic (2dQG) equation of meteorology. For the Navier-Stokes equation, our efforts will center on analyzing the self-similar solutions on a half-space or, possibly, a conical domain. Interest will be on their regularity and describing the solutions explicitly. For the MHD equations, research will center on the asymptotic behavior of solutions when dissipation is solely dependent on velocity. For the geo-strophic equations, the research will focus on describing the long-time behavior of flows around obstacles. Analysis of the Navier-Stokes equations is fundamental for understanding fluid flows. Any explicit solution helps in describing what possible flows can be sustained. The MHD equations arise when one adds the effect of a magnetic field and the fluid is assumed to contain electrically charged particles and ions. This project will investigate the solutions of these equations in the absence of magnetic dissipation. The analysis of the QG equations is a model for air-flow around an obstacle; a common problem in meteorology.