Qualitative Behavior of Turbulent Flows

Kukavica0604886这个项目涉及到Navier-Stokes方程的解，该方程是粘性不可压缩流体流动的主要模型。研究人员提出了关于正则性、解的定性行为(大小、复杂性、衰减性)、吸引子的定性描述、由可观测值确定解以及最小尺度的问题。欧拉方程、Kuramoto-Sivashinsky方程和复杂的Ginzburg-Landau型方程也有类似的问题。对流体流动动力学的了解在海洋学、大气科学、空气动力学和湍流理论等许多应用领域都是非常重要的。Navier-Stokes方程是研究粘性流体流动的主要模型。方程有着丰富的历史，由于其巨大的挑战性和与应用的直接联系，一直是一个热门的研究课题。调查者研究了正则性问题和解的定性行为。潜在的应用包括更好地理解湍流(涡旋、振荡)的微观结构，根据测量重建动力学，以及对流体运动的数值模拟进行严格的解释。

Kukavica0604886 This project is concerned with solutions of theNavier-Stokes equations, which are the principal model for flowof a viscous incompressible fluid. The investigator addressesquestions regarding regularity, qualitative behavior of solutions(size, complexity, decay), qualitative description of attractors,determination of solutions by observables, and minimal scale. Similar questions are addressed for the Euler equations,Kuramoto-Sivashinsky equation, and the complex Ginzburg-Landauequation. The understanding of dynamics of a fluid flow is importantin many applied fields, such as oceanography, atmosphericscience, aerodynamics, and turbulence theory. The Navier-Stokesequations are the main model for study of the viscous fluid flow. The equations have a rich history and have been a subject ofintense study due to their immense challenges and their directconnections with applications. The investigator studiesregularity questions and qualitative behavior of solutions. Potential applications include better understanding of smallstructures of turbulent flows (vortices, oscillations),reconstructing dynamics from measurements, and a rigorousinterpretation of numerical simulations of a fluid motion.