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On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations. (English) Zbl 1158.35074
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.
MSC:
35Q35PDEs in connection with fluid mechanics
35B40Asymptotic behavior of solutions of PDE
76A05Non-Newtonian fluids
76D05Navier-Stokes equations (fluid dynamics)