Applied Mathematics Colloquium: Dr. Yongjin Lu

Abstract: We study the pullback dynamics of 3D Navier-Stokes equations with nonlinear viscosity and subject to time-dependent external force. The pullback attractor attracts solutions to a dynamical system originated far enough in the past. Using a decomposition method, we establish the existence of a finite dimensional pullback attractor. We give estimates on the upper bound of the finite fractal dimension of pullback attractor. We also investigate the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.