As part of my doctoral studies, I am investigating the long-term behavior of stochastic partial differential equations (SPDEs). In particular, I am examining random dynamical systems, attractors, foliations, and invariant manifolds.
A general "rough path" is utilized as noise, which encompasses, in particular, the (fractional) Brownian motion. The resulting analytical view of the SPDEs enables a pathwise solution of the equation, which is a significant advantage for the consideration of the long-term behavior.
In further research projects, attractors for pathwise mild solutions of SPDEs as well as equations with boundary noise are investigate
Preprint
A. Blessing (Neamtu) and T. Seitz. Existence and regularity of random attractors for stochastic evolution equations driven by rough noise. arXiv:2401.14235
Publications
A. Neamtu and T. Seitz. Stochastic evolution equations with rough boundary noise. Partial Differ. Equ. Appl. 4, 49 (2023)