Local Properties of Turbulent Flows

本项目涉及流体动力学中出现的Navier-Stokes系统和其他方程解的局部性质。它讨论了通过观测确定偏微分方程的解，湍流中出现的不同长度尺度的描述和相互作用，以及不变流形的存在和性质。特别强调解的定性描述，例如解的时空复杂性、消失程度和流体涡旋性质的研究。流体动力学的问题出现在许多科学领域，包括大气科学、海洋学和空气动力学。Navier-Stokes系统是研究最广泛的偏微分方程组之一，是流体运动的主要模型之一。本项目探讨了Navier-Stokes系统及相关模型解的定性性质。潜在的应用包括更好地理解湍流的精细结构（漩涡和振荡），从测量中重建动力学，以及对流体运动数值模拟的严格解释。

This project concerns local properties of solutions of the Navier-Stokes system and other equations arising in fluid dynamics. It addresses determination of solutions of partial differential equations by observables, description and interplay of different length scales arising in turbulent flows, and existence and properties of invariant manifolds. Special emphasis is given to qualitative description of solutions, such as the study of spatial and temporal complexity of solutions, degree of vanishing, and properties of fluid vortices.Questions in fluid dynamics arise in many scientific fields, including atmospheric science, oceanography, and aerodynamics. The Navier-Stokes system, one of the most widely studied systems of partial differential equations, is one of the principal models of fluid motion. This project addresses qualitative properties of solutions of the Navier-Stokes system and related models. Potential applications include better understanding of fine structures of turbulent flows (vortices and oscillations), reconstruction of dynamics from measurements, and rigorous interpretation of numerical simulations of fluid motion.