M. Rockner

activity

19982026

most citedSPDE in Hilbert Space with Locally Monotone Coefficients

187 citations · 462 across the 62 of their papers we have counts for

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Showing 2025Show all

5 papers · 1 filter

math.PR2025

Sharp Non-uniqueness in Law for Stochastic Differential Equations on the Whole Space

Huaxiang Lü, Michael Röckner

In this paper, we investigate the stochastic differential equation on $R^{d}, d \geq 2$ : \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite…

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

Stochastic intrinsic gradient flows on the Wasserstein space

Panpan Ren, Michael Röckner, Feng-Yu Wang +1

We construct stochastic gradient flows on the $2$ -Wasserstein space $P_{2}$ over $R^{d}$ for energy functionals of the type $W_{F} (ρ d x) = \int_{R^{d}} F (x, ρ (x)) d x$ .…

math.AP2025

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…

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-…