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- W4289446345 abstract "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 apriori 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." @default.
- W4289446345 created "2022-08-02" @default.
- W4289446345 creator A5021171630 @default.
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- W4289446345 date "2022-07-29" @default.
- W4289446345 modified "2023-10-14" @default.
- W4289446345 title "On the norm equivalence of Lyapunov exponents for regularizing linear evolution equations" @default.
- W4289446345 doi "https://doi.org/10.48550/arxiv.2207.14797" @default.
- W4289446345 hasPublicationYear "2022" @default.
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