# Projects

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:
1. the regularity of the Navier-Stokes equations,
2. the symbiotic relations between the Navier-Stokes equations (or related differential equations such as the $\alpha$-Riccati equation, the Burgers equation, the KPP equation, the Montgomery-Smith equation) and the associated stochastic cascades,
3. numerical simulations and Monte Carlo simulations for fluid flows,
4. hydrodynamic stability.
• Publications:
1. 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).
2. 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).
3. 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).
4. Tuan Pham: “Global regularity criteria for the Navier-Stokes equations based on one approximate solution” (submitted, available online at arXiv:1910.05501).
5. Tuan Pham and Jared Whitehead: “Hydrodynamic stability in the presence of stochastic forcing” (in preparation)
6. Tuan Pham and Vladimir Sverak: “Minimal blow-up data for potential Navier-Stokes singularities in the half space” (in preparation).
7. Tuan Pham: “On the explosion problem of nonhomogeneous Yule cascades” (in preparation).
8. Tuan Pham: “Conservation of frequencies and the global regularity of the Navier-Stokes equations” (in preparation).
9. Tuan Pham: “Topics on the regularity theory of the Navier-Stokes equations” PhD thesis 2018.

Last updated: October 12, 2022