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2023 Center manifolds for rough partial differential equations
Christian Kuehn, Alexandra Neamţu
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Electron. J. Probab. 28: 1-31 (2023). DOI: 10.1214/23-EJP938


We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equations driven by nonlinear multiplicative noise, where the stochastic forcing is given by a γ-Hölder rough path, for γ(13,12]. Our proof technique relies upon the theory of rough paths and analytic semigroups in combination with a discretized Lyapunov-Perron-type method in a suitable scale of interpolation spaces. The resulting center manifold is a random manifold in the sense of the theory of random dynamical systems (RDS). We also illustrate our main theorem for reaction-diffusion equations as well as for the Swift-Hohenberg equation.


CK acknowledges support by a Lichtenberg Professorship. AN thanks Felix Hummel for helpful discussions regarding interpolation spaces.


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Christian Kuehn. Alexandra Neamţu. "Center manifolds for rough partial differential equations." Electron. J. Probab. 28 1 - 31, 2023.


Received: 12 January 2022; Accepted: 19 March 2023; Published: 2023
First available in Project Euclid: 28 March 2023

MathSciNet: MR4567460
zbMATH: 07707072
MathSciNet: MR4529085
Digital Object Identifier: 10.1214/23-EJP938

Primary: 37L55 , 60G22 , 60H15 , 60L20 , 60L50

Keywords: center manifold , evolution equation , interpolation spaces , Lyapunov-Perron method , rough path

Vol.28 • 2023
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