Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Rehmeier, Marco"'
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 motion is to the classical heat equation given by the (2-) Laplacian.
Externí odkaz:
http://arxiv.org/abs/2409.18744
Autor:
Rehmeier, Marco, Romito, Marco
In this note we contribute two results to the theory of the $2D$ Euler equations in vorticity form on the full plane. First, we establish a generalized Lagrangian representation of weak (in general measure-valued) solutions, which includes and extend
Externí odkaz:
http://arxiv.org/abs/2407.16609
Autor:
Flandoli, Franco, Rehmeier, Marco
This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of them deal with the effect on large scales of a small-scale perturbation o
Externí odkaz:
http://arxiv.org/abs/2402.16525
We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump L\'evy transport noise satisfies a dissipative deterministic equation involving a fractional Laplace-type operator. To this end, we i
Externí odkaz:
http://arxiv.org/abs/2402.08461
Autor:
Rehmeier, Marco
For the nonlinear Fokker--Planck equation $$\partial_tu = \Delta\beta(u)-\nabla \Phi \cdot \nabla \beta(u) - div_{\varrho}\big(D(x)b(u)u\big),\quad (t,x) \in (0,\infty)\times \mathbb{R}^d,$$ where $\varrho = \exp(-\Phi)$ is the density of a finite Bo
Externí odkaz:
http://arxiv.org/abs/2308.09420
Autor:
Rehmeier, Marco, Röckner, Michael
We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on $\mathbb{R}^d$ with a natural differential geometry. Our notion of gradient flow does not
Externí odkaz:
http://arxiv.org/abs/2306.09530
Autor:
Rehmeier, Marco, Röckner, Michael
We study nonlinear time-inhomogeneous Markov processes in the sense of McKean's seminal work [32]. These are given as families of laws $\mathbb{P}_{s,\zeta}$, $s\geq 0$, on path space, where $\zeta$ runs through a set of admissible initial probabilit
Externí odkaz:
http://arxiv.org/abs/2212.12424
Autor:
Kang, Myeongju, Rehmeier, Marco
We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique equilibri
Externí odkaz:
http://arxiv.org/abs/2205.13844
Autor:
Rehmeier, Marco
We provide a method to select flows of solutions to the Cauchy problem for linear and nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) for measures on Euclidean space. In the linear case, our method improves similar results of a previou
Externí odkaz:
http://arxiv.org/abs/2201.04539
Autor:
Rehmeier, Marco, Schenke, Andre
We study the incompressible hypodissipative Navier-Stokes equations with dissipation exponent $0 < \alpha < \frac{1}{2}$ on the three-dimensional torus perturbed by an additive Wiener noise term and prove the existence of an initial condition for whi
Externí odkaz:
http://arxiv.org/abs/2104.10798