TUOC PHAN

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Tuoc Phan
Tuoc Phan, Professor

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





Office: 224C 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 did my graduate study in the University of Minnesota (Twin Cities-Minnesota-US) and obtained my Ph.D. degree in 2007. 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. 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.

UTMJ

I am pleased to introduce the University of Tennessee Mathematical Journal (UTMJ), a newly launched research journal dedicated to the mathematics community. Operating on a non-profit, community-owned, and Diamond Open Access model, UTMJ remains entirely independent of commercial publishers.

I warmly welcome your manuscript submissions. Please feel free to reach out if you have any questions.

Preprints

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

  1. On linear elliptic equations with drift terms in critical weak spaces (with H. Kim and T.-P. Tsai), Communications in Contemporary Mathematics, (2026), [Journal article], [arXiv:2312.11215].
  2. Harnack inequality for singular or degenerate parabolic equations in non-divergence form (with S. Cho, and J. Fang), Journal of Differential Equations, Volume 457, 15 March 2026, 113997, [Journal article], [arXiv:2409.09437].
  3. An inviscid limit problem for Navier-Stokes equations in 3D domains with oscillatory boundaries (with Dario A. Valdebenito), Hiroshima Mathematical Journal (accepted, 2025), [arXiv:2503.06298].
  4. Sobolev estimates for singular-degenerate quasilinear equations beyond the \(A_2\) class (with H. Dong and Y. Sire), The Journal of Geometric Analysis, Volume 34, article number 286, (2024) [Journal article], [ arXiv:2305.07634].
  5. 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].
  6. 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].
  7. 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].
  8. 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].
  9. 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].
  10. A boundary layer problem in non-flat domains with measurable viscous coefficients (with Dario V. Castillo), Studies in Applied Mathematics, (2022), [Journal article].

Editorship

Others (for Vietnamese)

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