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Exponential mixing for stochastic 3D fractional Leray-\(\alpha\) model with degenerate multiplicative noise. (English) Zbl 07111304
Summary: In this work we establish the exponential mixing property for stochastic 3D fractional Leray-\(\alpha\) model with degenerate noise. The main result is also applicable to stochastic 3D hyperviscous Navier-Stokes equations and stochastic 3D critical Leray-\(\alpha\) model.

MSC:
60 Probability theory and stochastic processes
35 Partial differential equations
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[1] Leray, J., Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math., 63, 193-248, (1934) · JFM 60.0726.05
[2] Olson, E.; Titi, E. S., Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models, Nonlinear Anal., 6, 2427-2458, (2007) · Zbl 1110.76011
[3] Ali, H., On a critical Leray-\(\alpha\) model of turbulence, Nonlinear Anal. RWA, 14, 1563-1584, (2013) · Zbl 1261.35098
[4] Barbato, D.; Morandin, F.; Romito, M., Global regularity for a slightly supercritical hyperdissipative Navier-Stokes system, Anal. PDE, 7, 2009-2027, (2014) · Zbl 1309.76053
[5] Chueshov, I.; Millet, A., Stochastic 2D hydrodynamical type systems: well posedness and large deviations, Appl. Math. Optim., 61, 379-420, (2010) · Zbl 1196.49019
[6] Fernando, P. W.; Hausenblas, E.; Razafimandimby, P. A., Irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise, Comm. Math. Phys., 348, 535-565, (2016) · Zbl 1354.60067
[7] Liu, W.; Röckner, M., Stochastic Partial Differential Equations: An Introduction, (2015), Springer · Zbl 1361.60002
[8] S. Li, W. Liu, Y. Xie, Stochastic 3D Leray-\(\alpha\) model with fractional dissipation, arxiv:1805.11939.
[9] Hairer, M.; Mattingly, J. C., Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing, Ann. Math., 164, 993-1032, (2006) · Zbl 1130.37038
[10] Li, S.; Liu, W.; Xie, Y., Ergodicity of 3D Leray-\(\alpha\) model with fractional dissipation and degenerate stochastic forcing, Infinity Dimens. Anal. Quantum Probab. Relat. Top., 22, (2019) · Zbl 1447.60108
[11] Odasso, C., Exponential mixing for stochastic PDEs: the non-additive case, Probab. Theory Related Fields, 140, 41-82, (2008) · Zbl 1137.60030
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