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Award ID contains: 2009431

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  1. ; ; ; (, Physica D: Nonlinear Phenomena)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; (, Probability Theory and Related Fields)
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  3. ; (, Archive for Rational Mechanics and Analysis)
    We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differential equations, such equations are often posed on a scale of nonequivalent spaces mitigating, e.g., integrability (L^p) or differentiability (W^{s,p}). In contrast to finite dimensions, the Lyapunov exponent could a priori depend on the choice of norm used. In this paper we show that under quite general conditions, the Lyapunov exponent of a cocycle of compact linear operators is independent of the norm used. We apply this result to two important problems from fluid mechanics: the enhanced dissipation rate for the advection diffusion equation with ergodic velocity field; and the Lyapunov exponent for the 2d Navier–Stokes equations with stochastic or periodic forcing. 
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  4. ; ; (, The Annals of Probability)
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  5. ; (, Nonlinearity)
    Abstract Noise-induced order (NIO) is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish NIO for a natural class of systems of dimension ⩾ 2 consisting of a fiber-contracting skew product a over nonuniformly-expanding one-dimensional system. 
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  6. ; (, Annales de l'Institut Henri Poincaré C, Analyse non linéaire)
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  7. ; ; (, Journal of the European Mathematical Society)
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  8. ; ; (, The Annals of Probability)
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  9. ; ; (, Communications in Mathematical Physics)
    In this paper, we give a quantitative estimate for the first N Lyapunov exponents for random perturbations of a natural class of 2N-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but noninvariant subset of the phase space. Concrete models covered by our setting include systems of coupled standard maps, in both ‘weak’ and ‘strong’ coupling regimes. 
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