Global solutions and random dynamical systems for rough evolution equations

Robert Hesse; Alexandra Neamţu

doi:10.3934/dcdsb.2020029

Article Contents

2020, Volume 25, Issue 7: 2723-2748. Doi: 10.3934/dcdsb.2020029

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Global solutions and random dynamical systems for rough evolution equations

Robert Hesse^1, and
Alexandra Neamţu^2, ,

1.
Friedrich Schiller University Jena, Enst-Abbe-Platz 2, 07743, Jena, Germany
2.
Technical University of Munich, Boltzmannstr. 3, 85748, Garching bei München, Germany

^* Corresponding author: Alexandra Neamţu
^* Corresponding author: Alexandra Neamţu

Received: April 2019

Early access: April 2020

Published: July 2020

The authors are grateful to M. J. Garrido-Atienza and B. Schmalfuß for helpful comments. The authors also thank the referee for the valuable suggestions. AN acknowledges support by a DFG grant in the D-A-CH framework (KU 3333/2-1).

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Abstract

We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.

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Mathematics Subject Classification: 60H15, 60H05, 60G22, 37L55.

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References

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