Remarks on upper and lower bounds of solutions to the Navier–Stokes equations in R2

Dong, Bo-Qing and Chen, Zhi-Min (2006) Remarks on upper and lower bounds of solutions to the Navier–Stokes equations in R2. Applied Mathematics and Computation, 182 (1), 553-558. (doi:10.1016/j.amc.2006.04.017).

Abstract

In the study of long time asymptotic behaviors of the solutions of the two-dimensional Navier–Stokes equations in the whole space, some optimal upper and lower bounds for the decay of higher order derivatives of the solutions are derived through a simple approach without assuming any decay properties of the solutions. This method is mainly based on some auxiliary decay estimates of the solutions and a generalized Gronwall type argument.

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