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Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. (English) Zbl 1152.35012

In the present study the authors discuss the existence and regularity of pullback attractors for the following non-autonomous incompressible non-Newtonian fluid in 2D bounded domains:

u t+(u·)u+p=·τ(e(u))+g(x,t),x=(x 1 ,x 2 )Ω,(1)
·u=0,(2)

where Ω is a smooth bounded domain of 2 , u=u(x,t)=(u (1) (x,t),u (2) (x,t)), g(x,t)=g(t)=(g (1) (x,t),g (2) (x,t)), the scalar function p represents the pressure. Equations (1)–(2) describe the motion of an isothermal incompressible viscous fluid, where τ(e(u))=(τ ij (e(u))) 2×2 which is usually called the extra stress tensor of the fluid.


MSC:
35B41Attractors (PDE)
35Q35PDEs in connection with fluid mechanics
76D03Existence, uniqueness, and regularity theory