Departmental Colloquium
Mimi Dai
UIC
Long-time behavior of solutions to fluid equations
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.
Friday February 5, 2016 at 3:00 PM in SEO 636