※ 일시: 1-2강: 5월 28일(금) 9:00 - 11:00, 27동 220호
3-4강: 6월 4일(금): 9:00 - 10:30, 129동 301호
※ 1-2강: Nonuniqueness in law for stochastic hypodissipative NSE
The content of these talks is twofold: First, we give a brief introduction to the field of convex integration, tracing back the principal idea to its origin in a celebrated paper by John Nash on the isometric embedding problem for Riemannian manifolds.
From here, we review the major steps towards the recent seminal proof of the Onsager-conjecture by Isett et al. and also discuss convex integration in the realm of stochastic PDEs. Due to time restrictions, this part will have an overview and survey character. Secondly, we discuss a recent result obtained via convex integration methods, namely we prove ill-posedness in law of probabilistic strong solutions to the hypodissipative NSE with additive Brownian noise. This is joint work with Andre Schenke (Bielefeld University).
※ 3-4강: Superposition principle for stochastic nonlinear Fokker-Planck-Kolmogorov equations
We prove a superposition principle for nonlinear Fokker-Planck-Kolmogorov equations on Euclidean spaces and their corresponding linearized first-order continuity equation over the space of Borel (sub-)probability measures. As a consequence, we obtain equivalence of existence and uniqueness results for these equations. Moreover, we prove an analogous result for stochastically perturbed Fokker-Planck-Kolmogorov equations. To do so, we particularly show that such stochastic equations for measures are, similarly to the deterministic case, intrinsically related to linearized second-order equations on the space of Borel (sub-)probability measures.