V. Barbu

activity

20052026

most citedStochastic Porous Media Equation and Self-Organized Criticality

63 citations · 244 across the 55 of their papers we have counts for

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math.PR2026

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…

math.PR2025

The Leibenson process

Viorel Barbu, Sebastian Grube, Marco Rehmeier +1

Consider the Leibenson equation \begin{equation*} \partial_t u = Δ_p u^q, \end{equation*} where $Δ_{p} f = d i v (∣\nabla f ∣^{p - 2} \nabla f)$ for $p > 1$ and $q > 0$ , which is a simultaneous…

math.PR2025

Nonlinear Fokker-Planck equations as smooth Hilbertian gradient flows

Viorel Barbu, Michael Röckner

Under suitable assumptions on $β : R \to R, D : R^{d} \to R^{d}$ and $b : R^{d} \to R$ , the nonlinear Fokker-Planck equation $u_t-…

math.PR2024

$p$ -Brownian motion and the $p$ -Laplacian

Viorel Barbu, Marco Rehmeier, Michael Röckner

In this paper we construct a stochastic process, more precisely, a (nonlinear) Markov process, which is related to the parabolic $p$ -Laplace equation in the same way as Brownian mo…

math.PR2023

Uniqueness of distributional solutions to the 2D vorticity Navier-Stokes equation and its associated nonlinear Markov process

Viorel Barbu, Michael Röckner, Deng Zhang

In this work we prove uniqueness of distributional solutions to $2 D$ Navier-Stokes equations in vorticity form $u_{t} - ν Δ u + d i v (K (u) u) = 0$ on $(0, \infty) \times R^{2}$ with Radon…

math.PR2022

Recent progress on multi-bubble blow-ups and multi-solitons to (stochastic) focusing nonlinear Schrödinger equations