6 papers · 1 filter
Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure wi…
Nonlocal, nonlinear Fokker-Planck equations and nonlinear martingale problems
Viorel Barbu, José LuÃs da Silva, Michael Röckner
This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators , w…
Probabilistic representation of solutions to the parabolic -Laplace equation
Viorel Barbu, Michael Röckner
This work is concerned with the probabilistic representation of solutions to the -Laplace evolution equation …
Propagation of chaos for moderately interacting particle systems related to singular kinetic McKean-Vlasov SDEs
Zimo Hao, Jean-Francois Jabir, Stéphane Menozzi +2
This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by…
Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations
Huaxiang Lü, Michael Röckner, Xiangchan Zhu
We are concerned with the (stochastic) Lagrangian trajectories associated with Euler or Navier-Stokes equations. First, in the vanishing viscosity limit, we establish sharp non-uni…
The energy-critical stochastic Zakharov system
Sebastian Herr, Michael Röckner, Martin Spitz +1
This work is devoted to the stochastic Zakharov system in dimension four, which is the energy-critical dimension. First, we prove local well-posedness in the energy space $H^1\time…