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Several Continuities of a Pullback Random Attractor for Stochastic Non-Autonomous Zakharov Lattice Equations

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Abstract

We study the dynamics of stochastic Zakharov lattice equations driven by multiplicative white noise and time-dependent forces. We first deduce a cocycle (non-autonomous random dynamical system) on the product space of real and complex Hilbert spaces. We then prove the cocycle has a pullback random attractor parameterized by time and sample. We mainly establish several continuities including residual dense continuity, diagonally-invariant continuity, full stochastic continuity and full pre-continuity of the pullback random attractor on the time-sample plane with respect to the Hausdorff metric. The key point in the proof is to verify the time-space-sample continuity of the cocycle and local compactness of the pullback random attractor.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Yangrong Li & Lin Zhang

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Yangrong Li and Lin Zhang wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Yangrong Li.

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This work is supported by National Natural Science Foundation of China Grant 12271444.

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Li, Y., Zhang, L. Several Continuities of a Pullback Random Attractor for Stochastic Non-Autonomous Zakharov Lattice Equations. Qual. Theory Dyn. Syst. 23, 20 (2024). https://doi.org/10.1007/s12346-023-00874-0

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