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Random Attractors for 2D Stochastic Hydrodynamical-Type Systems

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Ukrainian Mathematical Journal Aims and scope

We study the asymptotic behavior of solutions to a class of abstract nonlinear stochastic evolution equations with additive noise that covers numerous 2D hydrodynamical models, such as the 2D Navier–Stokes equations, 2D Boussinesq equations, 2D MHD equations, etc., and also some 3D models, like the 3D Leray 𝛼-model. We prove the existence of random attractors for the associated continuous random dynamical systems. We also establish the upper semicontinuity of the random attractors as the parameter tends to zero.

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Authors and Affiliations

  1. Hanoi National University of Education, Hanoi, Vietnam

    C. T. Anh

  2. Hong Duc University, Thanh Hoa City, Vietnam

    N. T. Da

Authors
  1. C. T. Anh
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  2. N. T. Da
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Corresponding authors

Correspondence to C. T. Anh or N. T. Da.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 12, pp. 1647–1666, December, 2019.

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Anh, C.T., Da, N.T. Random Attractors for 2D Stochastic Hydrodynamical-Type Systems. Ukr Math J 71, 1888–1909 (2020). https://doi.org/10.1007/s11253-020-01754-5

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  • DOI: https://doi.org/10.1007/s11253-020-01754-5

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