TY - JOUR
T1 - Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term
AU - Cai , Yiting
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 1037
EP - 1053
PY - 2025
DA - 2025/05
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1037
UR - https://global-sci.org/intro/article_detail/jnma/24114.html
KW - Generalized Navier-Stokes equations, damping term, Fourier splitting method.
AB - <p style="text-align: justify;">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 $0 &lt; α &lt;\frac{3}{4}$ for any $β = 2.$ Secondly, for $0 &lt; α &lt; \frac{5}{4}$ and any $β &gt; {\rm max}\{ \frac{4α}{3}+1, 2\},$ we obtain the
same result.</p>