Dynamics of Partial Differential Equations
Volume 14 (2017)
Dynamics of a non-autonomous incompressible non-Newtonian fluid with delay
Pages: 375 – 402
We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of global solution is obtained by classical Galerkin approximation and the energy method. Actually, we also prove the uniqueness of solution as well as the continuous dependence on the initial value. Then we analyze the long time behavior of the dynamical system associated to the incompressible non-Newtonian fluid. Finally, we establish the existence of pullback attractors for the non-autonomous dynamical system associated to the problem.
incompressible non-Newtonian equation, pullback attractor, delay, the energy method
2010 Mathematics Subject Classification
Primary 35B40, 35Q35. Secondary 37L55, 76D03.
This research was partially supported by the projects MTM2015-63723-P (MINECO/FEDER, EU) and P12-FQM-1492 (Junta de Andalucía), and by NSF of China (Nos. 11671142 and 11371087), Science and Technology Commission of ShanghaiMunicipality (No. 13dz2260400) and Shanghai Leading Academic Discipline Project (No. B407), respectively.
Paper received on 23 April 2017.