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math.AP2025
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…
math.AP2024
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 str…
math.AP2024
Nonlinear Fokker--Planck--Kolmogorov equations as gradient flows on the space of probability measures
Marco Rehmeier, Michael Röckner
We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on with…