带非线性阻尼项g-Navier-Stokes方程的拉回指数吸引子Pullback exponential attractors for the g-Navier-Stokes equations with nonlinear damping
任丽宇,姜金平,刘生清,罗轩怡
摘要(Abstract):
研究具有非线性阻尼的二维g-Navier-Stokes方程的拉回指数吸引子存在问题.首先利用Galerkin方法证明一致拉回吸收集的存在性,然后利用能量方法证明解过程具有一致渐近紧性,最后证明拉回指数吸引子的存在性.
关键词(KeyWords): g-Navier-Stokes方程;拉回指数吸引子;非线性阻尼
基金项目(Foundation): 陕西省自然科学基础研究计划项目(2018JM1042);; 陕西省大学生创新创业计划训练项目(S202010719058)资助
作者(Author): 任丽宇,姜金平,刘生清,罗轩怡
参考文献(References):
- [1]CAI X,JIU Q.Weak and strong solutions for the incompressible Navier-Stokes equations with damping[J].Journal of Mathematical Analysis and Applications,2008,343(2):799-809.
- [2]ZHANG Z,WU X,LU M.On the uniqueness of strong solution to the incompressible Navier-Stokes equations with damping[J].Journal of Mathematical Analysis and Applications,2011,377(1):414-419.
- [3]ZHOU Y.Regularity and uniqueness for the 3D incompressible Navier-Stokes equations with damping[J].Applied Mathematics Letters,2012,25(11):1822-1825.
- [4]SONG X L,HOU Y R.Attractors for the three-dimensional incompressible Navier-Stokes equationswith damping[J].Discrete&Continuous Dynamical Systems-A,2011,31(1):239-252.
- [5]SONG X L,HOU Y R.Uniform attractors for three-dimensional Navier-Stokes equations with nonlinear damping[J].Journal of Mathematical Analysis&Applications,2015,422(1):337-351.
- [6]SONG X L,HOU Y.Rack D-attractors for three-dimensional Navier-Stokes equations with nonlinear damping[J].Boundary Value Problems,2016,2016(1):1-15.
- [7]PARDO D,VALERO J,Giménezá.Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping[J].Discrete&Continuous Dynamical Systems-B,2019,24(8):3569.
- [8]LI F,YOU B.Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping[J].Discrete&Continuous Dynamical Systems-B,2020,25(1):55.
- [9]LIU H,LIN L,SUN C,et al.The exponential behavior and stabilizability of the stochastic 3D Navier-Stokes equations with damping[J].Reviews in Mathematical Physics,2019,31(7):1950023.
- [10]彭小明,郑筱筱,尚亚东.具有非线性阻尼的Navier-Stokes-Voigt方程的拉回吸引子[J].数学物理学报,2021,41(2):357-369.
- [11]EDEN A,FOIAS C,NICOLAENKO B,et al.Exponential Attractors for Dissipative Evolution Equations[J].American Mathematical Monthly,1995,37(9):825-825.
- [12]CZAJA R,EFENDIEV M.Pullback exponential attractors for nonautonomous equations Part I:Semilinear parabolic problems[J].Journal of mathematical analysis and applications,2011,381(2):748-765.
- [13]José Langa,Miranville A,JoséReal.Pullback exponential attractors[J].Discrete&Continuous Dynamical Systems-Series A (DCDS-A),2017,26(4):1329-1357.
- [14]CARVALHO A N,SONNER S.Pullback exponential attractors for evolution processes in Banach spaces:properties and applications[J].Communications on Pure&Applied Analysis,2014,13(3):1141.
- [15]LI Y,WANG S,ZHAO T.The existence of pullback exponential attractors for nonautonomous dynamical system and applications to nonautonomous reaction diffusion equations[J].The Journal of Applied Analysis and Computation,2015,5(3):388-405.
- [16]韩英豪,周雪莹,傅雪,等.非自治Navier-Stokes方程的指数拉回吸引子[J].辽宁师范大学学报(自然科学版),2021,44(2):150-154.
- [17]SONG X L,HOU Y R.Attractors for the three-dimensional incompressible Navier-Stokes equations with damping[J].Discrete&Continuous Dynamical Systems,2011,31(1):239.
- [18]ROH J.Dynamics of the g-Navier-Stokes equations[J].Journal of Differential Equations,2005,211(2):452-484.
- [19]SONG H,WU H.Pullback attractors of nonautonomous reaction-diffusion equations[J].Journal of Mathematical Analysis and Applications,2007,325(2):1200-1215.