Tuoc Phan
Tuoc Phan, Professor

Department of Mathematics
University of Tennessee
403 Circle Drive, Knoxville TN 37996-1320

Office: 211 Ayres Hall
Email : tphan2 (at) utk dot edu
Phone: 865-974-4329

$$ \displaystyle{\left[\int_{-\infty}^T\left(\int_{\mathbb{R}^d_+}\big(|u|^p + |Du|^p\big)x_d^\gamma dx\right)^{q/p} dt \right]^{1/q} \leq N\left[\int_{-\infty}^T \left(\int_{\mathbb{R}^d_+} \big(|F|^p +|f|^p\big) x_d^\gamma dx\right)^{q/p} dt \right]^{1/q}}. $$

Welcome to Phan's homepage! I am a professor at the Department of Mathematics, The University of Tennessee-Knoxville. I grew up in Mekong Delta in Vietnam and I attended local schools there during my childhood. I went to college in Ho Chi Minh City (known as Sai Gon) and received the bachelor of science degree majoring in mathematics in 2000 from the University of Science. I did my graduate study in the University of Minnesota (Twin Cities-Minnesota-US) and obtained my Ph.D. degree in 2007. I was a postdoc at The University of British Columbia (2007 - 2010), and The University of Tennessee - Knoxville (2010 - 2012). My research is in partial differential equations. I study existence, uniqueness, and regularity estimates of solutions. I also work on nonlinear dynamics of solutions, and optimal control problems in mathematical biology. Growing up in a farm, I have a true love for gardening. I grow a tremendous amount of organic veggies and fruits every summer. I love walking, biking, and hiking, and enjoy hanging with friends at coffee shops, talking about mathematics. The math formula above is an a-priori estimate of the unknown solution \(u\) of a class singular-degenerate coefficient PDEs. This formula appears in my recent work, which is a joint work with Hongjie Dong and published here by the AMS. Additional information about me can be found in this article (in Vietnamese) published by Vietnamnet, and also in an interview video (in Vietnamese) in the #toan0mau series produced by professor H. V. Tran.


Recent Accepted/Published Papers (click here for the full list of Phan's publication)

  1. Nondivergence form degenerate linear parabolic equations on the upper half space (H. Dong and H. V. Tran), Journal of Functional Analysis (2024), [Journal article], [arXiv:2103.08033].
  2. On stationary Navier-Stokes equations in the upper-half plane (with Adrian D. Calderon and Van Le), Acta Applicandae Mathematicae (2024), [Journal article], [arXiv:2306.00319].
  3. Weighted mixed-norm \(L_p\)-estimates for equations in non-divergence form with singular coefficients: the Dirichlet problem (with H. Dong), Journal of Functional Analysis (2023), [Journal article], [arXiv:2103.08033].
  4. Degenerate linear parabolic equations in divergence form on the upper half space (with H. Dong and H. V. Tran), Transactions of the American Mathematical Society (2023), [Journal article], [arXiv:2107.08033].
  5. On trace theorems for weighted mixed norm Sobolev spaces and applications, Potentials and Partial Differential Equations: The Legacy of David R. Adams, Vol 8, Advances in Analysis and Geometry (2023), [arXiv:2205.04941].
  6. A boundary layer problem in non-flat domains with measurable viscous coefficients (with Dario V. Castillo), Studies in Applied Mathematics, (2022), [Journal article].
  7. On parabolic and elliptic equations with singular or degenerate coefficients (with H. Dong), Indiana University Mathematics Journal, accepted, [arXiv].
  8. Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients (with H. Dong and D. Kim), Communications in Partial Differential Equations, https://doi.org/10.1080/03605302.2022.2084627, arXiv:1910.00380, [arXiv].
  9. On higher integrability estimates for elliptic equations with singular coefficients (with J. Foldes), Funkcialaj Ekvacioj, 66 (2023), 1-16.[arXiv].
  10. On Masuda uniqueness theorem for Leray-Hopf weak solutions in mixed-norm spaces (with T. Robertson), European Journal of Mechanics / B Fluids, 90 (2021), 18-28 [Journal article], [preprint].


Others (for Vietnamese)

Coming Up