Tuoc Phan

Associate Professor

Department of Mathematics

University of Tennessee - Knoxville

** Office**: 205 Ayres Hall

** Email** : phan (at) math dot utk dot edu

** Phone**: 865-974-4329

Associate Professor

Department of Mathematics

University of Tennessee - Knoxville

Welcome to Dr. Phan's homepage! I am an associate professor at the Department of Mathematics, University of Tennessee-Knoxville. I received my B. S. degree in mathematics in 2000 from the University of Science (Ho chi Minh City-Vietnam), and my Ph.D. in 2007 from the University of Minnesota (Twin Cities-Minnesota-US). 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. I love outdoor activities (walking, biking, and hiking), and enjoy hanging with my family and friends at local coffee shops. I like gardening and regularly practice Taekwondo. The above math formula 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.

*Degenerate linear parabolic equations in divergence form on the upper half space*(with H. Dong and H. V. Tran), (2021), [arXiv:2107.08033], submitted.*On a class of divergence form linear parabolic equations with degenerate coefficients*(with H. V. Tran), (2021), [arXiv:2106.07637] (unpublished notes).*Weighted mixed-norm $L_p$ estimates for equations in non-divergence form with singular coefficients: the Dirichlet problem*(with H. Dong), submitted (2021), [arXiv:2103.08033].*On parabolic and elliptic equations with singular or degenerate coefficients*(with H. Dong), submitted, [arXiv].*Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients*(with H. Dong and D. Kim), arXiv:1910.00380, submitted, [arXiv].

*On higher integrability estimates for elliptic equations with singular coefficients*(with J. Foldes), Funkcialaj Ekvacioj, accepted, [arXiv].-
*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]. *Parabolic and elliptic equations with singular or degenerate coefficients: the Dirichlet problem*(with H. Dong), Transactions of the American Mathematical Society, https://doi.org/10.1090/tran/8397, [Journal article], [arXiv].-
*Mixed norm $L_p$-estimates for non-stationary Stokes systems with singular VMO coefficients and applications*(with H. Dong), Journal of Differential Equations, Volume 276, 5 (2021), 342-367, [Journal article], [arXiv]. *Regularity for parabolic equations with singular or degenerate coefficients*(with H. Dong), Calculus of Variations and Partial Differential Equations, 60, 44 (2021) Journal Article, [arXiv].*Weighted mixed-norm $L_p$-estimates for elliptic and parabolic equations in non-divergence form with singular degenerate coefficients*(with H. Dong), Revista Matemática Iberoamericana, DOI: 10.4171/rmi/1233, arXiv:1811.06393 [arXiv].*Existence uniqueness and regularity theory for elliptic equations with complex valued potentials*(with G. Todorova and B. Yordanov), Discrete and Continuous Dynamical Systems-Series A, 2021, 41(3): 1071-1099, [Journal article] [preprint].*Liouville type theorems for 3D stationary Navier-Stokes equations in weighted mixed-norm Lebesgue spaces*, Dynamics of Partial Differential Equations, Vol 17, no. 3 (2020), 229-243 [Journal article] [arXiv].*On well-posedness of 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces*(with Y. Sire), Analysis in Theory and Applications, 36 (2) (2020), 111-127 [Journal article] [preprint].

- Evolution Equations and Control Theory (since 06/2021)
- Electronic Journal of Differential Equations (since 07/2021)

- Phan's interview (in Vietnamese) in #toan0mau series.
- My lecture in Diễn Giải Toán Học 2020: video (in Vietnamese) and lecture notes.

- UTK-PDE Distinguished Lecture Series: Professor Irene Fonseca (CMU) will deliver 5 lectures (through zoom) at 2:50PM (US Eastern time) on November 18, December 2, 9 of 2021 and January 13, 20 of 2022. Register at UTK-PDE google form to receive zoom link information and reminder messages.