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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:

35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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