Sam Punshon-Smith

My research is focused the mathematical analysis and study of stochastic models arising in physical sciences. Much of my work involves the study long-time behavior and regularity properties of stochastic partial differential equations and infinite dimensional stochastic dynamics related to problems in fluids mechanics, kinetic theory and particle systems. Currently I am interested in the ergodic theory and chaotic mixing properties of the stochastic Navier-Stokes equations and the effect it has on statistics of passive scalar turbulence.

Publications

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

• "On the norm equivalence of Lyapunov exponents for regularizing linear evolution equations" (with A. Blumenthal). To Appear: Arch. Ration. Mech. Anal. (2023). [arXiv]
• "Chaos in stochastic 2d Galerkin-Navier-Stokes" (with J. Bedrossian). In: Comm. Math Phys. (2024). [arXiv]
• "Lower bounds on the Lyapunov exponents of stochastic differential equations" (with J. Bedrossian, A. Blumenthal). Proceedings of the AMS (2023). [arXiv]
• "A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations" (with J. Bedrossian, A. Blumenthal). In: Invent. Math. (2021). [arXiv]
• "The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics" (with J. Bedrossian, A. Blumenthal). In: Comm. Pure Appl. Math. (2021). [arXiv]
• "Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes" (with J. Bedrossian, A. Blumenthal). In: Probab Theory Relat Fields (2020). [arXiv]
• "Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations" (with J. Bedrossian, A. Blumenthal). In: Ann. Probab (2019). [arXiv]
• "Lagrangian chaos and scalar advection in stochastic fluid mechanics" (with J. Bedrossian, A. Blumenthal). In: J. Eur. Math. Soc. (2019). [arXiv]
• "Renormalized solutions to stochastic continuity equations with rough coefficients" (2019). [arXiv]
• "Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations" (with J. Bedrossian, M. Coti-Zelati, F. Weber). In: Arch. Ration. Mech. Anal. (2020). [arXiv]
• "A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations" (with J. Bedrossian, M. Coti-Zelati, F. Weber). In: Comm. Math Phys. (2018). [arXiv]
• "On the Boltzmann equation with stochastic kinetic transport: global existence of renormalized martingale solutions" (with S. Smith). In: Arch. Ration. Mech. Anal. (2018). [arXiv]