|
|
Navier-Stokes方程非阻尼极限研究
|
Abstract:
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。
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.
| [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. https://doi.org/10.1007/s000210050015 |
| [2] | Seregin, G. (2014) Lecture Notes on Regularity Theory for the Navier-Stokes Equations. World Scientific. https://doi.org/10.1142/9314 |
| [3] | Robinson, J.C., Rodrigo, J.L. and Sadowski, W. (2016) The Three-Dimensional Navier-Stokes Equations: Classical Theory. Cambridge University Press. https://doi.org/10.1017/cbo9781139095143 |
| [4] | Tsai, T. (2018) Lectures on Navier-Stokes Equations. American Mathematical Society. https://doi.org/10.1090/gsm/192 |
| [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. https://doi.org/10.1002/cpa.3160350604 |
| [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. https://doi.org/10.1016/j.jmaa.2008.01.041 |
| [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. https://doi.org/10.1515/math-2022-0050 |
| [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. https://doi.org/10.1016/j.jmaa.2009.04.027 |
