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Upper and lower bounds of temporal and spatial decays for the Navier-Stokes equations. (English) Zbl 1062.35058
The authors study the asymptotic behavior in the weighted \(L^2\) of solutions to the Navier-Stokes equations in the whole space \(\mathbb R^3\). Focussing on the decay problem for the weak solutions of the Navier-Stokes equations (first proposed by Leray for the Cauchy problem in \(\mathbb R^3\)) the authors obtain lower and upper bounds of the temporal-spatial decays by including appropriate weights and following the work of Shonbek and Miyakawa. The temporal-spatial decays for the Stokes flows with coresponding lower and upper bounds are also considered.

MSC:
35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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