Analytical Description of an Incompressible Flow

University Of Southern California, Los Angeles CA

Investigators

Abstract

The project addresses the qualitative properties of solutions to the Navier-Stokes, Euler, primitive, and other important equations in fluid dynamics. The spatial and temporal behavior of solutions, such as the size of solutions, spatial and temporal complexity, quantitative unique continuation, analytic and Gevrey regularity, and long time asymptotics, will be studied. The complex systems of equations involving coupling of the Navier-Stokes equations with elasticity and other equations will also be considered with emphasis on existence, uniqueness, regularity, and long time behavior of solutions. The Navier-Stokes and Euler equations are principal models for a fluid motion. The understanding of behavior of the solutions is of fundamental importance in engineering, meteorology, medicine, and oceanography. The project will address qualitative properties of solutions with special emphasis on the properties of fine structures in the flow including vortices and oscillations. The project will also address the relationship between large and small scale motion of fluids. The research will develop tools for better understanding of a turbulent fluid flow and will aim at finding relations between theory and numerical simulations.