Project A06
Dynamics and bifurcation theory of pathwise SPDEs

Project description

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. 

Principal Investigators

Alexandra Blessing (Neamţu, U Konstanz)

Nicolas Perkowski (FU Berlin)

Project members

Mazyar Ghani Varzaneh (U Konstanz)

Chara Zhu (FU Berlin)

Publications

• Blessing Neamţu, A. & Ghani Varzaneh, M. (2026). An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients. Electronic Journal of Probability, 31: 1-49. https://doi.org/10.1214/26-EJP1526

• Blessing (Neamţu), A., Rosati, T. 2026. Quantitative instability for stochastic scalar reaction-diffusion equations. The Annals of Applied Probability, 36(2). https://doi.org/10.1214/25-AAP2255

• Ghani Varzaneh, M., Riedel, S., 2026. Invariant manifolds and stability for rough differential equations. Journal of Mathematical Analysis and Applications, 556(1), 130112. https://doi.org/10.1016/j.jmaa.2025.130112

• Ghani Varzaneh, M., & Riedel, S., 2025. Singular stochastic delay equations driven by fractional Brownian motion: Dynamics, longtime behaviour, and pathwise stability. Electronic Journal of Probability, 30. https://doi.org/10.1214/25-EJP1440

• Blessing, A., Ghani Varzaneh, M., Seitz, T. 2025. A mild rough Gronwall lemma with applications to non-autonomous evolution equations. Stochastics and Partial Differential Equations: Analysis and Computations. https://doi.org/10.1007/s40072-025-00402-y

• Ghani Varzaneh, M., Lahbiri, F. Z., Riedel, S. 2025. Invariant manifolds for random parabolic evolution equations with almost sectorial operators. Stochastics and Dynamics, 25(06), 2530001. https://doi.org/10.1142/S0219493725300013

→ Stochastics and Dynamics Best Papers Award 2025

• 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

Preprints

• Blessing Neamtu, A., Crisan, D., & Lang, O., 2026. Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise. https://doi.org/10.48550/ARXIV.2604.05910 

• Blessing, A., & Ghani Varzaneh, M., 2026. Synchronization by noise for stochastic differential equations driven by fractional Brownian motion. https://doi.org/10.48550/arXiv.2603.12774 

• Blessing, A., Perkowski, N., & Zhu, C. 2026. Renormalization destroys a finite time bifurcation in the $Φ^4_2$ equation. https://doi.org/10.48550/arXiv.2602.08460 

• Blessing, A., Blömker, D. 2025. On the approximation of finite-time Lyapunov exponents for the stochastic Burgers equation. https://doi.org/10.48550/ARXIV.2510.09460

• Blessing, A., Rudik, D. 2025. Taylor-like approximations of center manifolds for rough differential equations.https://doi.org/10.48550/ARXIV.2510.00971

• Blessing, A., Ghani Varzaneh, M. 2025. On the negativity of the top Lyapunov exponent for stochastic differential equations driven by fractional Brownian motion. https://doi.org/10.48550/ARXIV.2510.11531

• 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 

Preprints prior to this CRC relevant to the project

• Blessing, A., Rosati, T., 2024. Quantitative instability for stochastic scalar reaction-diffusion equations. https://doi.org/10.48550/ARXIV.2406.04651