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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 9 (1997), S. 307-341 
    ISSN: 1572-9222
    Keywords: Random attractors ; stochastic dynamical systems ; deterministic nonautonomous systems ; stochastic Navier-Stokes equation ; stochastic Burgers equation ; stochastic nonlinear wave equation ; 58F11 ; 58F12 ; 60H15 ; 34D45 ; 35Q30 ; 35Q35 ; 35L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we generalize the notion of an attractor for the stochastic dynamical system introduced in [7]. We prove that the stochastic attractor satisfies most of the properties satisfied by the usual attractor in the theory of deterministic dynamical systems. We also show that our results apply to the stochastic Navier-Stokes equation, the white noise-driven Burgers equation, and a nonlinear stochastic wave equation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 102 (1995), S. 367-391 
    ISSN: 1432-2064
    Keywords: 60H15 ; 76D05 ; 35Q10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.
    Type of Medium: Electronic Resource
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