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Zbl 1059.35104
Dong, Boqing; Li, Yongsheng
Large time behavior to the system of incompressible non-Newtonian fluids in $\bbfR^2$. (English)
[J] J. Math. Anal. Appl. 298, No. 2, 667-676 (2004). ISSN 0022-247X

From the text: We consider the optimal decay rate of global solutions to the Cauchy problem for two-dimensional non-Newtonian fluids $$u_t-\Delta u+ (u\cdot\nabla)u- \nabla\cdot (|e(u)|^{p-2}e(u))+ \nabla\pi= 0,$$ $$\nabla\cdot u=0, \qquad u(x,0)= u_0.$$ It is proved that the weak solutions decay in $L^2$ norm at $(1+t)^{-1/2}$ and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
76A05 Non-Newtonian fluids
35B40 Asymptotic behavior of solutions of PDE

Keywords: weak solutions

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