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Volume 7, Issue 3
Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term

Yiting Cai

J. Nonl. Mod. Anal., 7 (2025), pp. 1037-1053.

Published online: 2025-05

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

37L05, 35Q35, 35B40

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COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1037, author = {Cai , Yiting}, title = {Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {3}, pages = {1037--1053}, abstract = {

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} }
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 -

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.

Cai , Yiting. (2025). Decay of Solutions to the Three-Dimensional Generalized Navier-Stokes Equation with Nonlinear Damping Term. Journal of Nonlinear Modeling and Analysis. 7 (3). 1037-1053. doi:10.12150/jnma.2025.1037
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