Discipline: Mathematics & Statistics
Subcategory: STEM Research
Yongjin Lu - Virginia State University
We study the long time behavior of Navier-Stokes equation when it is subject to time dependent external force. More specifically, (a). We study the regularity of strong uniform attractors for 3D viscoelastic incompressible fluid flow subject to Kelvin-Voigt damping and a time dependent translation bounded external force. (b) We then study the pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external force. The main result established is the existence of finite-dimensional pullback attractors in a general setting involving tempered universes. In addition, we present a sufficient condition on the viscosity coefficients that guarantees the nontrivial-ness of the attractors. We also show the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.
Funder Acknowledgement(s): National Science Foundation, HBCU-UP, Research Initiation Award (No 1601127)
Faculty Advisor: None Listed,