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Zbl 1158.35074
Dong, Bo-Qing; Chen, Zhi-Min
On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations. (English)
[J] J. Math. Anal. Appl. 334, No. 2, 1386-1399 (2007). ISSN 0022-247X

The purpose of this paper is to show the upper-lower bound estimate for the $L^2$-decay rates of higher-order derivatives of solutions to the micropolar fluid motion equations. To this end, the authors examine the decay estimates of derivatives for the solutions to the linearized micropolar fluid motion equations and then extend the estimates on linearized equations to the nonlinear equations by using a generalized Gronwall type argument.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
35B40 Asymptotic behavior of solutions of PDE
76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: micropolar fluid motion equations; upper and lower bounds; $L^{2}$ decay

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