Research

My research focuses on the interplay of noise, mixing, and chaos in fluid dynamics, utilizing tools from stochastic analysis, dynamical systems, and PDEs to address challenging problems in turbulence theory. My work often centers on two intertwined themes: the mixing properties of passive scalars advected by random flows, and the emergence and quantification of chaos in high- and infinite-dimensional systems. These themes are deeply connected, as the chaotic behavior of the underlying flow plays a crucial role in driving efficient mixing.

Publications

My preprints and publications are available at my ArXiv Page, and my Research Gate profile.

Submitted

  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2025). Non-uniqueness and unique selection of stationary measures for the degenerately forced stochastic Lorenz-96. [arXiv] New!
  • Hairer, M., Punshon-Smith, S., Rosati, T., & Yi, J. (2024). Lower bounds on Lyapunov exponents for linear PDEs driven by the 2D stochastic Navier-Stokes equations. [arXiv] New!
  • Bedrossian, J., Flyn, P., & Punshon-Smith, S. (2024). Low regularity mixing for random volume preserving diffeomorphisms. [arXiv] New!

Published

  • Bedrossian, J., & Punshon-Smith, S. (2024). Chaos in Stochastic 2d Galerkin-Navier-Stokes. Communications in Mathematical Physics, 405, 107. [arXiv]
  • Blumenthal, A., & Punshon-Smith, S. (2023). On the Norm Equivalence of Lyapunov Exponents for Regularizing Linear Evolution Equations. Archive for Rational Mechanics and Analysis, 247, 97. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2023). Lower bounds on the Lyapunov exponents of stochastic differential equations. Proceedings of the International Congress of Mathematicians. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2022). A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations. Inventiones Mathematicae, 227, 429-516. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2022). The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number. Communications on Pure and Applied Mathematics, 75, 1237-1291. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2022). Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations. The Annals of Probability, 50, 241-303. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2022). Lagrangian chaos and scalar advection in stochastic fluid mechanics. Journal of the European Mathematical Society, 24, 1893-1990. [arXiv]
  • Bedrossian, J., Blumenthal, A., & Punshon-Smith, S. (2021). Almost-sure enhanced dissipation and uniform- in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes. Probability Theory and Related Fields , 179, 777-834. [arXiv]
  • Bedrossian, J., Coti-Zelati, M., Punshon-Smith, S., & Weber, F. (2020). Sufficient Conditions for Dual Cascade Flux Laws in the Stochastic 2d Navier-Stokes Equations. Archive for Rational Mechanics and Analysis , 237, 103-145. [arXiv]
  • Bedrossian, J., Coti-Zelati, M., Punshon-Smith, S., & Weber, F. (2019). A Sufficient Condition for the Kolmogorov 4/5 Law for Stationary Martingale Solutions to the 3D Navier-Stokes Equations. Communications in Mathematical Physics, 367, 1045-1075. [arXiv]
  • Punshon-Smith, S. (2019). "Renormalized solutions to stochastic continuity equations with rough coefficients". [arXiv]
  • Punshon-Smith, S., & Smith, S. (2018). On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions. Archive for Rational Mechanics and Analysis, 229, 627-708. [arXiv]