187 citations · 462 across the 62 of their papers we have counts for
11 papers · 1 filter
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 …
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…
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…
Nonlocal, nonlinear Fokker-Planck equations and nonlinear martingale problems
Viorel Barbu, José Luís 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 , whe…
Second order fractional mean-field SDEs with singular kernels and measure initial data
Zimo Hao, Michael Röckner, Xicheng Zhang
In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernel…