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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Springer US

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DOI

10.1002/chin.200438095

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1572-9222

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Random Attractor Associated with the QuasiGeostro

Authors: RongChan Zhu XiangChan Zhu
Publish Date: 2016/05/20
Volume: 29, Issue: 1, Pages: 289-322
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Abstract

We study the long time behavior of the solutions to the 2D stochastic quasigeostrophic equation on mathbb T2 driven by additive noise and real linear multiplicative noise in the subcritical case ie alpha frac12 by proving the existence of a random attractor The key point for the proof is the exponential decay of the Lpnorm and a bootstrapping argument The upper semicontinuity of random attractors is also established Moreover if the viscosity constant is large enough the system has a trivial random attractorThe following Lemma is a technical result from 16 Lemma 5 Let X n be a sequence of real random variables indexed by n Let fmathbb Z+rightarrow mathbb R+ Define the random variable T mathrmboundX nf to be the smallest positive integer such that mT mathrmboundX nfRightarrow X mfm

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. A Grobman–Hartman Theorem for Control Systems
  3. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  4. Second Order Abstract Neutral Functional Differential Equations
  5. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  6. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  7. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  8. Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition
  9. A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
  10. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  11. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  12. On The Number of Characteristic Lines for Homogeneous Vector Fields
  13. Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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