Tao Yan , Lu Zhang , Aihong Zou , Ji Shu . DYNAMICS OF THE STOCHASTIC $g$-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE^*[J]. Acta mathematica scientia, Series B, 2023 , 43(5) : 2108 -2120 . DOI: 10.1007/s10473-023-0511-y

[1] Bates P W, Lu K, Wang B. Random attractors for stochastic reaction diffusion equations on unbounded domains. J Differential Equations, 2009, 246: 845-869
[2] Bae H O, Roh J. Existence of solutions of the $g$-Navier-Stokes equations. Taiwanese J Math, 2004, 8: 85-102
[3] Beyn W J, Gess B, Lescot P, et al. The global random attractor for a class of stochastic porous media equations. Comm Partial Differential Equations, 2011, 36: 446-469
[4] Capinski M, Cutland N J. Existence of global stochastic flow and attractors for Navier-Stokes equations. Probab Theory Related Fields, 1999, 115: 121-151
[5] Caraballo T, Garrido-Atienza M J, Schmalfuss B, et al. Non-autonomous and random attractors for delay random semilinear equations without uniqueness. Discrete Contin Dyn Syst, 2008, 21: 415-443
[6] Caraballo T, Real J, Chueshov I D. Pullback attractors for stochastic heat equations in materials with memory. Discrete Contin Dyn Syst Ser B, 2008, 9: 525-539
[7] Caraballo T, Langa J A.On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems. Dyn Contin Discrete Impuls
Syst Ser A Math Anal, 2003, 10: 491-513
[8] Caraballo T, Garrido-Atienza M J, Schmalfuss B, et al. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete Contin Dyn Syst Ser B, 2010, 14: 439-455
[9] Caraballo T, Garrido-Atienza M J, Taniguchi T. The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. Nonlinear Anal, 2011, 74: 3671-3684
[10] Caraballo T, Langa J A, Melnik V S, et al. Pullback attractors of nonautonomous and stochastic multivalued dynamical systems. Set-Valued Anal, 2003, 11: 153-201
[11] Chueshov I, Millet A. Stochastic 2D hydrodynamical type systems: well posedness and large deviations. Appl Math Optim, 2010, 61: 379-420
[12] Chueshov I, Scheutzow M. On the structure of attractors and invariant measures for a class of monotone random systems. Dyn Syst, 2004, 19: 127-144
[13] Chueshov I.Monotone Random Systems Theory and Applications. Lecture Notes in Mathematics, Vol 1779. Berlin: Springer-Verlag, 2002
[14] Crauel H, Debussche A, Flandoli F. Random attractors. J Dynam Differential Equations, 1997, 9: 307-341
[15] Crauel H, Flandoli F. Attractors for random dynamical systems. Probab Theory Related Fields, 1994, 100: 365-393
[16] Flandoli F, Schmalfuss B. Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise. Stochastics Stochastics Rep, 1996, 59: 21-45
[17] Garrido-Atienza M J, Schmalfuss B. Ergodicity of the infinite dimensional fractional Brownian motion. J Dynam Differential Equations, 2011, 23: 671-681
[18] Garrido-Atienza M J, Ogrowsky A, Schmalfuss B. Random differential equations with random delays. Stoch Dyn, 2011, 11: 369-388
[19] Garrido-Atienza M J, Maslowski B, Schmalfuss B. Random attractors for stochastic equations driven by a fractional Brownian motion. Internat J Bifur Chaos Appl Sci Engrg, 2010, 20: 2761-2782
[20] Gess B, Liu W, Rockner M. Random attractors for a class of stochastic partial differential equations driven by general additive noise. J Differential Equations, 2011, 251: 1225-1253
[21] Gess B. Random attractors for degenerate stochastic partial differential equations. J Dynam Differential Equations, 2013, 25: 121-157
[22] Gess B. Random attractors for singular stochastic evolution equations. J Differential Equations, 2013, 255: 524-559
[23] Kloeden P E, Langa J A. Flattening, squeezing and the existence of random attractors. Proc R Soc Lond Ser A Math Phys Eng Sci, 2007, 463: 163-181
[24] Kloeden P E, Rasmussen M. Nonautonomous Dynamical Systems.Mathematical Surveys and Monographs, Vol 176. Providence: American Mathematical Society, 2011
[25] Ladyzhenskaya O.New equations for the description of the viscous incompressible fluids and solvability in large of the boundary value problems for them//Boundary Value Problems of Mathematical Physics. Providence: American Mathematical Society, 1970
[26] Roh J.$g$-Navier-Stokes Equations[D]. Minnesota: University of Minnesota, 2001
[27] Schmalfuss B.Backward cocycles and attractors of stochastic differential equations//International Seminar on Applied Mathematics-Nonlinear Dynamics: Attractor Approximation and Global Behavior. Dresden, 1992: 185-192
[28] Wang B. Random attractors for the stochastic Benjamin-Bona-Mahony equation on unbounded domains. J Differential Equations, 2009, 246: 2506-2537
[29] Wang B. Asymptotic behavior of stochastic wave equations with critical exponents on $ \mathbb{R}^{3} $. Trans Amer Math Soc, 2011, 363: 3639-3663
[30] Wang B. Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems. J Diffferential Equations, 2012, 253: 1544-1583
[31] Wang B. Weak pullback attractors for mean random dynamical systems in Bochner spaces. J Dynam Differential Equations, 2019, 31: 2177-2204
[32] Wang B. Dynamics of stochastic reaction-diffusion lattice systems driven by nonlinear noise. J Math Anal Appl, 2019, 477: 104-132
[33] Wang B. Weak pullback attractors for stochastic Navier-Stokes equations with nonlinear diffusion terms. Proc Amer Math Soc, 2019, 147: 1627-1638
[34] Wang R, Guo B, Wang B. Well-posedness and dynamics of fractional FitzHugh-Nagumo systems on $\mathbb{R}^{N}$ driven by nonlinear noise. Sci China Math, 2020, 64(11): 2395-2436
[35] Prato G D, Zabczyk J.Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press, 1992
[36] Zhao W, Zhang Y. Upper semi-continuity of random attractors for a non-autonomous dynamical system with a weak convergence condition. Acta Math Sci, 2020, 40B(4): 921-933