分数阶不可压缩Navier-Stokes-Coriolis方程周期解的存在性
Existence of Periodic Solutions to the Fractional Navier-Stokes-Coriolis Equation
摘要: 本文研究了带有旋转效应的分数阶Navier-Stokes方程在给定周期外力作用下周期mild解的存在唯一性，并且建立了Besov空间中分数阶热半群的线性估计。首先，给出符号及函数空间的定义。其次，采用分数阶热半群的Lp-Lq估计，分别对分数阶不可压缩Navier-Stokes-Coriolis方程的线性项及非线性项进行了估计。最后证明了给定一个具有周期ω的外力f，分数阶不可压缩Navier-Stokes-Coriolis方程周期mild解是唯一存在的，且周期也为ω。
Abstract: In this paper, we study the existence and uniqueness of periodic mild solution for fractional incompressible Navier-Stokes equations in the rotational framework and establish the linear estimation of fractional heat semigroups in Besov space. Firstly, the definition of symbol and function space is given. Secondly, the linear and nonlinear terms of the fractional incompressible Navier-Stokes-Coriolis equations were estimated by using the Lp-Lq estimates of fractional heat semigroups. Finally, we proved that given an external force with periodic ω, the periodic mild solution of the fractional incompressible Navier-Stokes-Coriolis equation is uniqueness and its period is also ω.
文章引用：何港晶, 孙小春. 分数阶不可压缩Navier-Stokes-Coriolis方程周期解的存在性[J]. 应用数学进展, 2022, 11(1): 193-203. https://doi.org/10.12677/AAM.2022.111024

参考文献

[1] Hieber, M. and Shibata, Y. (2010) The Fujita-Kato Approach to the Navier-Stokes Equations in the Rotational Framework. Mathematische Zeitschrift, 265, 481-491. [Google Scholar] [CrossRef] 
[2] Zhao, H.Y. and Wang, Y.X. (2017) A Remark on the Navier-Stokes Equations with the Coriolis Force. Mathematical Methods in the Applied Sciences, 40, 7323-7332. [Google Scholar] [CrossRef] 
[3] Wang, W.H. and Wu, G. (2018) Global Mild Solution of the Generalized Navier-Stokes Equations with Coriolis Force. Applied Mathematics Letters, 76, 181-186. [Google Scholar] [CrossRef] 
[4] Iwabuchi, T. and Takada, R. (2018) Time Periodic Solutions to the Navier-Stokes Equations in the Rotational Framework. Journal of Evolution Equations, 12, 985-1000. [Google Scholar] [CrossRef] 
[5] Sun, X.C. and Ding, Y. (2020) Dispersive Effect of the Coriolis Force and the Local Well Posedness for the Navier-Stokes-Coriolis System. Journal of Evolution Equations, 20, 335-354. [Google Scholar] [CrossRef] 
[6] Kishimoto, N. and Yoneda, T. (2018) Global Solvability of the Rotating Navier-Stokes Equations with Fractional Laplacian in a Periodic Domain. Mathematische Annalen, 372, 743-779. [Google Scholar] [CrossRef] 
[7] Wang, W.H. and Wu, G. (2018) Global Mild Solution of Stochastic Generalized Navier-Stokes Equations with Coriolis Force. Acta Mathematica Sinica, English Series, 34, 1635-1647. [Google Scholar] [CrossRef] 
[8] Kozono, H. and Nakao, M. (1996) Periodic Solutions of Navier-Stokes Equations in Unbounded Domains. Tohoku Mathematical, 48, 33-50. [Google Scholar] [CrossRef] 
[9] Sun, X.C. and Liu, J. (2021) Global Well-Posedness for the Fractional Navier-Stokes-Coriolis Equations in Function Spaces Characterized by Semigroups. Preprint. [Google Scholar] [CrossRef] 
[10] Miao, C.X., Yuan, B.Q. and Zhang, B. (2008) Well-Posedness of the Cauchy Problem for the Fractional Power Dissipative Equations. Nonlinear Analysis: Theory, Methods & Applications, 68, 461-484. [Google Scholar] [CrossRef] 
[11] Kozono, H., Ogawa, T. and Taniuchi, Y. (2003) Navier-Stokes Equations in the Besov Space near and BMO. Kyushu Journal of Mathematics, 57, 303-324. [Google Scholar] [CrossRef] 
[12] Sun, X.C. and Ding, Y. (2015) Strichartz Estimates for Parabolic Equations with Higher Order Differential Operator. Science China Mathematics, 58, 1047-1062. [Google Scholar] [CrossRef] 
[13] Bahouri, H., Chemin, J.Y. and Danchin, R. (2011) Fourier Analysis and Nonlinear Partial Differential Equations. Grundlehren der Mathematischen Wissenschaften, Springer, New York. [Google Scholar] [CrossRef] 

为你推荐