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. singularities of the complex Burgers equation,
  4. numerical simulations and Monte Carlo simulations for fluid flows,
  5. hydrodynamic stability of plane Couette flow and Rayleigh-Bénard convection.

• Seminar lectures
• Gallery
• Instructions for BYUH Research Assistants:
  1. Set up workspace
  2. Install Inkscape with LaTeX extension
  3. Integrate Wolfram Language into JupyterLab

• Publications:
  1. Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Navier-Stokes Equations with Fractional Dissipation and Associated Doubly Stochastic Yule Cascades” (available online at arXiv:2509.10806).
  2. Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: “Transformation of Stochastic Recursions and Critical Phenomena in the Analysis of the Aldous-Shields-Athreya Cascade and Related Mean Flow Equations” (submitted, available online at arXiv:2411.00629).
  3. 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).
  4. 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).
  5. 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).
  6. 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).
  7. Tuan Pham: “Global regularity criteria for the Navier-Stokes equations based on one approximate solution” (submitted, available online at arXiv:1910.05501).
  8. Tuan Pham and Jared Whitehead: “Hydrodynamic stability in the presence of stochastic forcing” (in preparation)
  9. Tuan Pham and Vladimir Sverak: “Minimal blow-up data for potential Navier-Stokes singularities in the half space” (in preparation).
  10. Tuan Pham: “On the explosion problem of nonhomogeneous Yule cascades” (in preparation).
  11. Tuan Pham: “Conservation of frequencies and the global regularity of the Navier-Stokes equations” (in preparation).
  12. Tuan Pham: “Topics on the regularity theory of the Navier-Stokes equations” PhD thesis 2018.
  13. 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

• Other research works:
  1. Complex Burgers singularities
  2. Linear PDE with constant coefficients

_{Last updated: Sep 18, 2025}