Mimi Dai : Long-time behavior of solutions to fluid equations

Posted by Brooke Shipley , part of the Departmental Colloquium.

At

Feb. 5, 2016, 3 p.m.

In

SEO 636

Abstract

An important feature of dissipative systems is the existence of the global attractor that describes the long-time behavior of all the solutions. When the spacial domain is not bounded and Poincaré’s inequality is not valid, the existence of the global attractor is still an open question. However, when the force is small, one can prove that the global attractor is a unique fixed point using the Fourier splitting method. We apply this method to study the long-time behavior of solutions to various fluid equations including the Navier-Stokes, and certain complex fluid models, such as the liquid crystal systems, and obtain optimal decay rates for the solutions.