Open Collections

Stability of equilibria and existence of pullback attractors for delay 2D Navier-Stokes equations

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we will show several methods to analyze the long time behaviour of solutions to 2D Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, mem- ory, etc) appear in the formulation. First the existence, uniqueness and local stability analysis of steady-state solutions is studied by using several methods: the theory of Lyapunov functions, the Razumikhin- Lyapunov technique, by constructing appropriate Lyapunov functionals and finally by using a method based in Gronwall-like inequalities. Then the global asymptotic behaviour of solutions can be analyzed by using the theory of attractors. As the delay terms are allowed to be very general, the statement of the problem becomes nonautonomous in gen- eral. For this reason, the theory of nonautonomous pullback attractors appears to be appropriate.

Mathematics; Partial differential equations; Calculus of variations and optimal control; optimization

video/mp4

Author affiliation: Universidad de Sevilla

2016-03-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/57143

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/