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Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces
We study the three-dimensional incompressible Navier--Stokes equations with a componentwise nonlinear damping term of the form $α\sum_{k=1}^3 u_k^{2m+1}e_k$ in Fourier and Fourier-- Gevrey spaces based on $\mathcal{X}^0(\mathbb{R}^3)$. We first establish local-in-time existence and uniqueness of sol
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