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3D Navier-Stokes equations of power law type with damping

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Abstract

We establish the existence of unique strong solutions to non-Newtonian Navier-Stokes equations of power law type with damping in three dimensions and moreover, that the solution has \(L^2\) decay rate

$$\begin{aligned} \Vert u(t)\Vert _{L^2(\mathbb {R}^3)}^2\lesssim (1 + t)^{-\min \{m-1,\frac{5}{2}(-m+2\mu )-1\}}, \quad \forall \, t> 0, \end{aligned}$$

for \(m > 1\) and \(\frac{m}{2}- \frac{1}{2}< \mu < \frac{m}{2}- \frac{1}{5}\).

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Acknowledgements

Jae-Myoung Kim’s work is supported by a Research Grant of Andong National University

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  1. Department of Mathematics Education, Andong National University, Andong, 36729, Republic of Korea

    Jae-Myoung Kim

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Kim, JM. 3D Navier-Stokes equations of power law type with damping. Arch. Math. 118, 323–335 (2022). https://doi.org/10.1007/s00013-021-01684-z

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