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| Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term |
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| KeyWord:Generalized Navier-Stokes equations, damping term, Fourier splitting method |
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| Abstract: |
| In this paper, we consider the three-dimensional generalized Navier-Stokes equation with a nonlinear damping term $|u|^{\beta-1}(\beta\ge1)$. Firstly, utilizing the Fourier splitting method, we derive decay estimates for weak solutions to the equations when $\alpha=0$ and $\beta=1$, as well as when $0<\alpha<\frac{3}{4}$ for any $\beta=2$. Secondly, for $0<\alpha<\frac{5}{4}$ and any $\beta>\max\{\frac{4\alpha}{3}+1,2\}$, we obtain the same result. |
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