Fluid Flows at Large

拟议研究摘要maria E. Schonbek这个项目是继续分析流体力学的三个基本方程的工作。这些是流体力学的Navier-Stokes方程和磁流体动力学方程（MHD）和气象学的二维准地转方程（2dQG）。对于Navier-Stokes方程，我们的工作将集中在分析半空间或可能的圆锥域上的自相似解。人们的兴趣在于它们的规律性和对解的明确描述。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，研究将侧重于描述绕障流动的长期行为。对Navier-Stokes方程的分析是理解流体流动的基础。任何显式的解决方案都有助于描述哪些可能的流可以持续。当一个人加上磁场的影响，并且假定流体中含有带电粒子和离子时，MHD方程就出现了。本项目将研究这些方程在无磁耗散情况下的解。QG方程的分析是一个绕障气流模型；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.