Qualitative studies of the Navier-Stokes and related systems

该项目研究流体力学中的Navier-Stokes方程和相关方程的解的定性性质，包括Euler方程和原始方程。我们将通过估计解的复杂性来研究湍流中小尺度的性质，并研究它与流体中可观测性和自由度问题的关系。相当大的努力将致力于流体结构模型(局部和整体的存在性、正则性)和其他涉及流体边界的复杂偏微分方程组。我们还将研究海洋和大气的粘性和无粘性原始方程的性质解。我们将特别感兴趣的是解的局部和全局的存在性及其渐近行为。流体的数学研究在气象学、科学和工程中具有重要的基础意义。该项目寻求更好地了解流体运动，特别是在与湍流有关的小尺度上。将特别强调构成天气预报基本模式的原始方程，以及模拟流体与弹性体相互作用的流体-结构系统。

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.