The project aims to analyze the asymptotic behavior of rough and singular stochastic partial differential equations, especially at bifurcations, using finite-time Lyapunov exponents and amplitude equations for bifurcation analysis. It also develops a theory of attractors and investigates the convergence speed to invariant measures, focusing on describing mixing times in hydrodynamic limits.
Mazyar Ghani Varzaneh (U Konstanz)
Xiaohan Zhu (FU Berlin)
Agresti, A., Blessing (Neamţu), A., Luongo, E., 2025. Global well-posedness of 2D Navier–Stokes with Dirichlet boundary fractional noise. Nonlinearity 38, 075023. https://doi.org/10.1088/1361-6544/ade21c
Ghani Varzaneh, M., Riedel, S., Schmeding, A., Tapia, N., 2025. The geometry of controlled rough paths. Stochastic Processes and their Applications 184, 104594. https://doi.org/10.1016/j.spa.2025.104594
Blessing (Neamţu), A., Blumenthal, A., Breden, M., Engel, M., 2025. Detecting random bifurcations via rigorous enclosures of large deviations rate functions. Physica D: Nonlinear Phenomena 476, 134617. https://doi.org/10.1016/j.physd.2025.134617
Berglund, N., Blessing (Neamţu), A., 2025. Concentration estimates for SPDEs driven by fractional Brownian motion. Electron. Commun. Probab. 30. https://doi.org/10.1214/25-ECP664
Blessing, A., Varzaneh, M.G., 2025. An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients. https://doi.org/10.48550/ARXIV.2503.04415
Blessing, A., Varzaneh, M.G., Seitz, T., 2025. A mild rough Gronwall Lemma with applications to non-autonomous evolution equations. https://doi.org/10.48550/ARXIV.2503.03628
Blessing, A., Seitz, T., Sonner, S., Tang, B.Q., 2025. Pathwise mild solutions for superlinear stochastic evolution equations and their attractors. https://doi.org/10.48550/ARXIV.2502.01209
Varzaneh, M.G., Riedel, S., 2024. Singular stochastic delay equations driven by fractional Brownian motion: Dynamics, longtime behaviour, and pathwise stability. https://doi.org/10.48550/ARXIV.2411.04590
Blessing, A., Rosati, T., 2024. Quantitative instability for stochastic scalar reaction-diffusion equations. https://doi.org/10.48550/ARXIV.2406.04651