Navier-Stokes方程非阻尼极限研究
Study on the Undamped Limit of Navier-Stokes Equations
摘要: 本论文对Navier-Stokes方程非阻尼极限进行了研究，即对带有阻尼项的Navier-Stokes方程解的极限行为进行研究。证明了在相同初值条件下，带有不同阻尼项的Navier-Stokes方程的解u均收敛到Navier-Stokes方程的解v。
Abstract: In this paper, the undamped limit of Navier-Stokes equation is studied, that is, the limit behavior of the solution of Navier-Stokes equation with damped term is studied. It is proved that the solutions of Navier-Stokes equations with different damping terms converge to the solutions of Navier-Stokes equations under the same initial value conditions.
文章引用：刘爱博, 王晓燕. Navier-Stokes方程非阻尼极限研究[J]. 应用数学进展, 2024, 13(9): 4275-4288. https://doi.org/10.12677/aam.2024.139408

参考文献

[1] Ladyzhenskaya, O.A. and Seregin, G.A. (1999) On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional Navier-Stokes Equations. Journal of Mathematical Fluid Mechanics, 1, 356-387. [Google Scholar] [CrossRef] 
[2] Seregin, G. (2014) Lecture Notes on Regularity Theory for the Navier-Stokes Equations. World Scientific. [Google Scholar] [CrossRef] 
[3] Robinson, J.C., Rodrigo, J.L. and Sadowski, W. (2016) The Three-Dimensional Navier-Stokes Equations: Classical Theory. Cambridge University Press. [Google Scholar] [CrossRef] 
[4] Tsai, T. (2018) Lectures on Navier-Stokes Equations. American Mathematical Society. [Google Scholar] [CrossRef] 
[5] Caffarelli, L., Kohn, R. and Nirenberg, L. (1982) Partial Regularity of Suitable Weak Solutions of the Navier‐Stokes Equations. Communications on Pure and Applied Mathematics, 35, 771-831. [Google Scholar] [CrossRef] 
[6] Cai, X. and Jiu, Q. (2008) Weak and Strong Solutions for the Incompressible Navier-Stokes Equations with Damping. Journal of Mathematical Analysis and Applications, 343, 799-809. [Google Scholar] [CrossRef] 
[7] Zhou, Y. (2012) Regularity and Uniqueness for the 3D Incompressible Navier-Stokes Equations with Damping. Applied Mathematics Letters, 25, 1822-1825.
[8] Benameur, J. (2022) Global Weak Solution of 3D-NSE with Exponential Damping. Open Mathematics, 20, 590-607. [Google Scholar] [CrossRef] 
[9] Benameur, J. and Ltifi, M. (2021) Strong Solution of 3D-NSE with Exponential Damping. arXiv: 2103.16707.
[10] Guo, B. and Guo, C. (2009) The Convergence of Non-Newtonian Fluids to Navier-Stokes Equations. Journal of Mathematical Analysis and Applications, 357, 468-478. [Google Scholar] [CrossRef] 

为你推荐