Weak and strong solutions for the incompressible Navier-Stokes equations with damping

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Abstract

In this paper, we show that the Cauchy problem of the Navier-Stokes equations with damping α | u |β - 1 u(α > 0) has global weak solutions for any β ≥ 1, global strong solution for any β ≥ 7 / 2 and that the strong solution is unique for any 7 / 2 ≤ β ≤ 5. © 2008 Elsevier Inc. All rights reserved.

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Cai, X., & Jiu, Q. (2008). Weak and strong solutions for the incompressible Navier-Stokes equations with damping. Journal of Mathematical Analysis and Applications, 343(2), 799–809. https://doi.org/10.1016/j.jmaa.2008.01.041

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