9 papers
Uniqueness for nonlinear Fokker-Planck equations with general diffusion terms and their associated nonlinear Markov processes
Viorel Barbu, Yuqi Li, Michael Röckner
This work is concerned with the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with non-diagonal diffusion terms of type \begin{equation} u_{t}-\sum_{i…
Wasserstein regularity of vorticity solutions to the 2D Navier-Stokes equations
Viorel Barbu
One proves that the the vorticity flow of 2D Navier Stokes equation can be identified with an absolutely continuous curve in Wasserstein space W_{p} where p\in [1,2}.
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 …
The Leibenson process
Viorel Barbu, Sebastian Grube, Marco Rehmeier +1
Consider the Leibenson equation \begin{equation*} \partial_t u = Î_p u^q, \end{equation*} where for and , which is a simultaneo…
Nonlinear Fokker-Planck equations with singular integral drifts and McKean-Vlasov SDEs
Viorel Barbu
One proves the well-posedness in the Sobolev space H^{-1} of nonlinear Fokker-Planck equations with singular drifts.Applications to existence of strong solutions to McKean-Vlasov e…