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Non-uniqueness of Leray--Hopf solutions for the fractional Navier--Stokes equations perturbed by transport noise
Theresa Lange, Marco Rehmeier, Andre Schenke
For the fractional Navier--Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically stro…
-Brownian motion and the -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 -Laplace equation in the same way as Brownian mo…
vorticity Euler equations: Superposition solutions and nonlinear Markov processes
Marco Rehmeier, Marco Romito
In this note we contribute two results to the theory of the Euler equations in vorticity form on the full plane. First, we establish a generalized Lagrangian representation of…
Average dissipation for stochastic transport equations with Lévy noise
Franco Flandoli, Andrea Papini, Marco Rehmeier
We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump Lévy transport noise satisfies a dissipative deterministic equa…
Remarks on regularization by noise, convex integration and spontaneous stochasticity
Franco Flandoli, Marco Rehmeier
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 the…