Large time behavior of a third grade fluid system. (English) Zbl 1374.35072
Summary: We consider the large time behavior of a non-autonomous third grade fluid system, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem admits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.
MSC:
35B41 | Attractors |
37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
76D05 | Navier-Stokes equations for incompressible viscous fluids |