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 -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.

• Seminar lectures
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• BYUH Research Assistants: set up workspace

• Publications:
  1. Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Erratum to Stochastic explosion and non-uniqueness for -Riccati equation”. Journal of Mathematical Analysis and Applications, Vol 527, Issue 2. (Also available online at arXiv:2103.06912).
  2. Radu Dascaliuc, Tuan Pham and Enrique Thomann: “On Le Jan-Sznitman’s stochastic approach to the Navier-Stokes equations”. Transactions of the American Mathematical Society, Vol 377, No. 4, 2335-2365, April 2024. (Also available online at arXiv:1910.05500).
  3. 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).
  4. Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Doubly Stochastic Yule Cascades (Part II): The explosion problem in the non-reversible case”. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, No. 4, Vol 59, 1904-1933, 2023. (Also available online at arXiv:2107.13182).
  5. Tuan Pham: “Global regularity criteria for the Navier-Stokes equations based on one approximate solution” (submitted, available online at arXiv:1910.05501).
  6. Tuan Pham and Jared Whitehead: “Hydrodynamic stability in the presence of stochastic forcing” (in preparation)
  7. Tuan Pham and Vladimir Sverak: “Minimal blow-up data for potential Navier-Stokes singularities in the half space” (in preparation).
  8. Tuan Pham: “On the explosion problem of nonhomogeneous Yule cascades” (in preparation).
  9. Tuan Pham: “Conservation of frequencies and the global regularity of the Navier-Stokes equations” (in preparation).
  10. Tuan Pham: “Topics on the regularity theory of the Navier-Stokes equations” PhD thesis 2018.

• Other publications (conference papers):
  1. D. Nguyen, T. Pham and Q. Phan, “A Semantic Model for Building the Vietnamese Language Query Processing Framework in e-Library Searching Application,” in 2nd International Conference on Machine Learning and Computing, Bangalore, 2010 pp. 179-183. doi:10.1109/ICMLC.2010.17

_{Last updated: June 15, 2024}