8 papers
The Incompressible Navier--Stokes--Fourier System with Thermal Noise
Benjamin Gess, Max Sauerbrey, Zhengyan Wu
We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible determini…
Probabilistically Strong Solutions to Stochastic Euler Equations
Benjamin Gess, Robert Lasarzik
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergen…
Existence of martingale solutions to a stochastic kinetic model of chemotaxis
Benjamin Gess, Sebastian Herr, Anne Niesdroy
We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions…
Stabilization by transport noise and enhanced dissipation in the Kraichnan model
Benjamin Gess, Ivan Yaroslavtsev
Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a s…
The Porous Medium Equation: Large Deviations and Gradient Flow with Degenerate and Unbounded Diffusion
Benjamin Gess, Daniel Heydecker
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic parti…
Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting
Benjamin Gess, Sebastian Kassing
We prove explicit bounds on the exponential rate of convergence for the momentum stochastic gradient descent scheme (MSGD) for arbitrary, fixed hyperparameters (learning rate, fric…