Tuoc Phan’s homepage

Associate Professor

Department of Mathematics

University of Tennessee – Knoxville

227 Ayres hall, 1403 Circle Drive

Knoxville, TN 37996



Contact information:


      Office:   225 Ayres hall

      Tel:       865-974-4329

      Email:  tphan2 at utk.edu

      Fax:     (865) - 974 - 6576



Research interests: Partial Differential Equations

v  Existence uniqueness and regularity theory estimates: Linear, nonlinear, elliptic parabolic equations and system of equations, nonlinear p-Laplacian equations, equations with singular degenerate coefficients, Navier-Stokes equations.

v  Nonlinear dynamics in nonlinear dispersive equations: Asymptotical stability of solitons in Dirac equations, Klein-Gordon equations, and Schrödinger  equations.

v  Optimal control and its applications in mathematical biology: Population (cells, chemical concentration) dynamics in heteronomy. My work provides potential optimal methods for treatment and managements.


Curriculum vitae: [PDF],            Research statement: [PDF],           Teaching statement:  [PDF]



Recent papers:


                    I.         Submitted

1.      Liouville type theorems for 3D stationary Navier-Stokes equations in weighted mixed-norm Lebesgue spaces, 12pp., arXiv:1812.10135 [arXiv].

2.      Weighted mixed-norm L_p-estimates for elliptic and parabolic equations in  non-divergence form with singular degenerate coefficients (with H. Dong), submitted, 27 pp.,  arXiv:1811.06393 [arXiv].

3.      Existence uniqueness and regularity theory for elliptic equations with complex valued potentials (with G. Todorova and B. Yordanov), submitted (2018), [preprint].

4.      Mixed norm Lp-estimates for non-stationary Stokes systems with singular VMO coefficients and applications (with H. Dong), 20 pp., submitted, [arXiv].

5.      On higher integrability estimates for elliptic equations with singular coefficients (with Juraj Foldes), 10 pp. submitted, [arXiv].

6.      Regularity theory for parabolic equations with singular degenerate coefficients  (with H. Dong), 31p., submitted, [arXiv].

                  II.         Accepted/puplished

1.      Well-posedness for the Navier-Stokes equations in critical mixed-norm Lebesgue spaces, Journal of Evolution Equations, [Author shared link] [Journal article],  arXiv:1903:08319 [arXiv].

2.      Weighted Calderon-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations, Potential Analysis,  DOI: 10.1007/s11118-018-9737-z  [Author shared link][Journal article], [arXiv].

3.      Free energy in mean field of Brownian particle (with X. Chen), Discrete and Continuous Dynamical Systems – Series A, 39 (2019), no. 2, 747-769, [Journal article] [preprint].

4.      Weighted W1,p-estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable (with Tadele Mengesha), Nonlinear Analysis, Vol. 179 (2019), p. 184-236 https://doi.org/10.1016/j.na.2018.08.012 [Journal article][arXiv].

5.      Interior gradient estimates for weak solutions of quasi-linear p-Laplacian type equations, Pacific journal of Mathematics, 297-1 (2018), 195--224. DOI 10.2140/pjm.2018.297.195, [preprint] [Journal article].

6.      Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients (with Dat Cao and Tadele Mengesha), AMS Contemporary Mathematics, 18 pp., accepted, [preprint], [arXiv].

7.      Lorentz estimates for weak solutions of quasi-linear parabolic equations with singular divergence-free drifts, Canadian Journal of Mathematics, DOI:10.4153/CJM-2017-049-3, [preprint].

8.      Weighted W1,p-estimates for weak solutions of degenerate and singular elliptic equations (with Dat Cao and Tadele Mengesha), Indiana University Mathematics Journal, Vol. 67, No. 6 (2018), 2225-2277, [arXiv] [Journal version].

9.      Regularity estimates for BMO-weak solutions of quasi-linear equations with inhomogeneous boundary conditions, Nonlinear Differential Equations and Applications NoDEA, 49 pp., DOI: 10.1007/s00030-018-0501-2, [preprint][Journal version].

10.    Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations, Journal of Differential Equations 263 (2017) 8329-8361, doi.org/10.1016/j.jde.2017.08.043, [Journal paper], [arXiv].


Complete list of publication: list of publication and preprints


Grants:  Simons collaboration (2015-2020), grant #354889.

Upcoming Events: None

CAAM’s information: Conference on Analysis and Applied Mathematics, Ho Chi Minh City University of Technology (Hutech), January 3 – 4, 2019.