Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term (Journal of Nonlinear Modeling and Analysis, 2025)
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 solutionsto the equations when $α = 0$ and $β = 1,$ as well as when $0 < α {\rm max}\{ \frac{4α}{3}+1, 2\},$ we obtain thesame result.
Keywords: Generalized Navier-Stokes equations; damping term; Fourier splitting method.