Qualitative studies of the Navier-Stokes and related systems

该项目涉及Navier-Stokes方程和流体动力学中相关方程（包括欧拉方程和原始方程）解的定性性质。我们将通过估计解的复杂性来研究湍流中小尺度的性质，并研究与流体中可观测量和自由度问题的关系。一个相当大的努力将致力于一个流体结构模型（局部和整体存在，规律性）和其他复杂的PDE系统涉及流体边界。我们还将研究海洋和大气的粘性和无粘性原始方程的解的性质。我们将特别感兴趣的是局部和整体的存在性及其渐近行为。流体的数学研究在气象学，科学和工程学中具有根本的重要性。该项目旨在更好地了解流体运动，特别是在湍流中感兴趣的小尺度上。特别强调的是要放在原始方程，构成天气预报的基本模型和流体与弹性体的相互作用的流体-结构系统建模。

The project addresses qualitative properties of solutions of the Navier-Stokes and related equations arising in fluid dynamics, including the Euler and Primitive equations. We will investigate the properties of small scales in a turbulent flow by estimating the complexity of solutions and study the relationship with the problems regarding observables and degrees of freedom in a fluid. A considerable effort will be dedicated to a fluid-structure models (local and global existence, regularity) and other complex PDE systems involving a fluid boundary. We will also study the properties solutions of the viscous and inviscid primitive equation of the ocean and the atmosphere. We will especially be interested in local and global existence of solutions and their asymptotic behavior.The mathematical study of fluids is of fundamental importance in meteorology, science, and engineering. The project seeks better understanding of the fluid motion especially on small scales which are of interest in turbulence. The special emphasis is going to be placed on the primitive equations which constitute the basic model for weather prediction and on the fluid-structure systems modeling interaction of a fluid with an elastic body.