J. Nonl. Mod. Anal., 7 (2025), pp. 1037-1053.
Published online: 2025-05
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In this paper, we consider the three-dimensional generalized Navier-Stokes equation with a nonlinear damping term $|u|^{β−1} (β ≥ 1).$ Firstly, utilizing the Fourier splitting method, we derive decay estimates for weak solutions to the equations when $α = 0$ and $β = 1,$ as well as when $0 < α <\frac{3}{4}$ for any $β = 2.$ Secondly, for $0 < α < \frac{5}{4}$ and any $β > {\rm max}\{ \frac{4α}{3}+1, 2\},$ we obtain the same result.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1037}, url = {http://global-sci.org/intro/article_detail/jnma/24114.html} }In this paper, we consider the three-dimensional generalized Navier-Stokes equation with a nonlinear damping term $|u|^{β−1} (β ≥ 1).$ Firstly, utilizing the Fourier splitting method, we derive decay estimates for weak solutions to the equations when $α = 0$ and $β = 1,$ as well as when $0 < α <\frac{3}{4}$ for any $β = 2.$ Secondly, for $0 < α < \frac{5}{4}$ and any $β > {\rm max}\{ \frac{4α}{3}+1, 2\},$ we obtain the same result.