Analytical Description of an Incompressible Flow

该项目解决了流体动力学中Navier-Stokes， Euler， primitive和其他重要方程的解的定性性质。将研究解的时空行为，如解的大小，时空复杂性，定量唯一延拓，解析和Gevrey正则性以及长时间渐近性。同时，还将考虑具有弹性的Navier-Stokes方程与其他方程耦合的复杂方程组，重点是解的存在性、唯一性、规律性和长时间行为。Navier-Stokes方程和Euler方程是流体运动的主要模型。对溶液行为的理解在工程、气象学、医学和海洋学中是至关重要的。该项目将讨论溶液的定性性质，特别强调流中的精细结构的性质，包括漩涡和振荡。该项目还将解决大尺度和小尺度流体运动之间的关系。这项研究将开发工具，以更好地理解湍流流体的流动，并将致力于寻找理论和数值模拟之间的关系。

The project addresses the qualitative properties of solutions to the Navier-Stokes, Euler, primitive, and other important equations in fluid dynamics. The spatial and temporal behavior of solutions, such as the size of solutions, spatial and temporal complexity, quantitative unique continuation, analytic and Gevrey regularity, and long time asymptotics, will be studied. The complex systems of equations involving coupling of the Navier-Stokes equations with elasticity and other equations will also be considered with emphasis on existence, uniqueness, regularity, and long time behavior of solutions.The Navier-Stokes and Euler equations are principal models for a fluid motion. The understanding of behavior of the solutions is of fundamental importance in engineering, meteorology, medicine, and oceanography. The project will address qualitative properties of solutions with special emphasis on the properties of fine structures in the flow including vortices and oscillations. The project will also address the relationship between large and small scale motion of fluids. The research will develop tools for better understanding of a turbulent fluid flow and will aim at finding relations between theory and numerical simulations.