Stochastic Fluid Dynamics

Main fields of application

Stochastic fluid dynamics studies the interaction of nonlinear transport, dissipation and random forcing in fluids and interfaces. We analyse models in which noise represents thermal fluctuations, unresolved scales or random transport.

Our work includes stochastic Euler and Navier–Stokes-type equations, coupled thermal systems, stochastic thin-film models and geometric SPDEs for fluctuating interfaces. We investigate existence, regularity, energy balances, ergodicity and large deviations, with special attention to conservative and physically consistent noise. Analytical results are paired with structure-preserving numerical questions so that approximations retain key conservation laws and geometric features.

Current directions

  • Stochastic Euler and Navier–Stokes equations
  • Thermal and transport noise
  • Fluctuating interfaces and thin films
  • Geometric SPDEs
  • Energy, regularity and large deviations

Related people

Related projects

Selected publications

  • Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks

    Published · Computer Methods in Applied Mechanics and Engineering 462, 119289 (2026). Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy — faithfully capturing complex physical behavior governed by differential equations. In…

  • The Incompressible Navier–Stokes–Fourier System with Thermal Noise

    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 deterministic setting the equation for the velocity can be solved independently of the temperature, the inclusion of the effects of…

  • Probabilistically Strong Solutions to Stochastic Euler Equations

    In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier–Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically strong solutions for the stochastic incompressible Euler equations. In particular, this solves the…

  • Ergodicity for SPDEs driven by divergence-free transport noise

    We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the uniqueness of invariant probability measures, even…

  • A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise

    The celebrated De Giorgi-Nash-Moser theory ensures that solutions to uniformly elliptic or parabolic PDEs are bounded and Hölder continuous, even with merely bounded measurable coefficients. For parabolic SPDEs with transport noise, boundedness has recently been established, but Hölder continuity remains a key…

  • Existence of martingale solutions to a stochastic kinetic model of chemotaxis

    Published · Nonlinear differential equations and applications, 33 (2026) 2, p. 52. 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 on the turning kernel and…

  • Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality

    Accepted / forthcoming · Annals of Applied Probability. The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise intensity and correlation length. This proves the consistency of the large…

  • Solutions to the stochastic thin-film equation for initial values with non-full support

    Published · Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383. The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on…