Qualitative Behavior of Turbulent Flows

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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.