Random attractors for rough stochastic partial differential equations

摘要

This paper is devoted to the existence of random attractors for rough partial differential equations driven by nonlinear multiplicative Holder rough paths with exponents in (1/3, 1/2]. Our approach relies upon rough paths theory and stopping times analysis in a suitable scale of interpolation spaces. The core step is to derive the adequate algebraic and analytical properties of a sequence of stopping times, which allows us to establish the required compact tempered absorbing set. The existence of a pullback attractor for the generated random dynamical system is straightforward. An illustrative example is presented by reaction-diffusion equations subjected to fractional Brownian rough paths.& COPY; 2023 Elsevier Inc.

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