North British Probability Seminar – Events
Upcoming Seminars and Events: (NBPS runs on Tuesday afternoons from 2.05 pm to 3 pm in the academic year 24/25)
Tuesday, June 10, 2025
Theresa Lange (Scuola Normale Superiore Pisa)
Time: 2.05 – 3.00 pm
Location: JCMB 5323
Title: Non-uniqueness of Leray-Hopf solutions for the 3D fractional Navier-Stokes equations perturbed by transport noise
Abstract:
For the 3D fractional Navier-Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically strong Leray-Hopf solutions. In the deterministic case, global existence is known ever since the seminal works by Leray (1934) and Hopf (1950), yet recent results show non-uniqueness via the method of convex integration. In contrast to the active field of regularisation by transport noise, we demonstrate that the convex integration method applies also in the presence of such random perturbations, and derive global-in-time solutions which satisfy the energy inequality pathwise on a non-empty random interval [0, tau].
This is joint work with Marco Rehmeier (TU Berlin) and Andre Schenke. The activity was carried out within the project: NoisyFluid “Noise in Fluids”, Grant Agreement 101053472, CUP E53C22001720006.
Kotaro Tsugawa(Chuo University)
Time: 3.05 – 4.00 pm
Location: JCMB 5323
Title: Cancellations and unconditional well-posedness of fifth-order KdV-type and fifth-order modified KdV-type equations
Abstract:
The fifth-order KdV and fifth-order modified KdV equations are known as the second equations in the integrable KdV and mKdV hierarchies, respectively. In this study, we consider these equations with general coefficients, including non-integrable cases, and establish local well-posedness with unconditional uniqueness. A major difficulty arises from the presence of third-order derivatives in the nonlinear terms. To address this, we apply normal form reduction to the resonant parts and exploit cancellations arising from an appropriate algebraic transformation in the non-resonant parts. This is joint work with Takamori Kato.
