My research fields are Partial Differential Equations, Probability, Fluid Dynamics, and Numerical Analysis. I investigate differential equations from analytic, probabilistic, and numerical perspectives. If you are interested to be involved in a project, either at an undergraduate or graduate level, please feel free to contact me.
- My current projects are on:
- the regularity of the Navier-Stokes equations,
- the symbiotic relations between the Navier-Stokes equations (or related differential equations such as the -Riccati equation, the Burgers equation, the KPP equation, the Montgomery-Smith equation) and the associated stochastic cascades,
- numerical simulations and Monte Carlo simulations for fluid flows,
- hydrodynamic stability.
- Radu Dascaliuc, Tuan Pham and Enrique Thomann: “On Le Jan-Sznitman’s stochastic approach to the Navier-Stokes equations” (submitted, available online at arXiv:1910.05500).
- Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Doubly Stochastic Yule Cascades (Part I): The explosion problem in the time-reversible case”. Journal of Functional Analysis, Vol 284, Issue 1, 2023. (Also available online at arXiv:2103.06912).
- Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Doubly Stochastic Yule Cascades (Part II): The explosion problem in the non-reversible case”. To appear on Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. (Also available online at arXiv:2107.13182).
- Tuan Pham: “Global regularity criteria for the Navier-Stokes equations based on one approximate solution” (submitted, available online at arXiv:1910.05501).
- Tuan Pham and Jared Whitehead: “Hydrodynamic stability in the presence of stochastic forcing” (in preparation)
- Tuan Pham and Vladimir Sverak: “Minimal blow-up data for potential Navier-Stokes singularities in the half space” (in preparation).
- Tuan Pham: “On the explosion problem of nonhomogeneous Yule cascades” (in preparation).
- Tuan Pham: “Conservation of frequencies and the global regularity of the Navier-Stokes equations” (in preparation).
- Tuan Pham: “Topics on the regularity theory of the Navier-Stokes equations” PhD thesis 2018.
Last updated: October 12, 2022