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.      Parabolic and elliptic equations with singular or degenerate coefficients:  the Dirichlet problem (with H. Dong), submitted, [arXiv].

2.      On parabolic and elliptic equations with singular or degenerate coefficients (with H. Dong), [arXiv].

3.      Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients (with H. Dong and D. Kim), submitted, arXiv:1910.00380 [ArXiv].

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].

                  II.         Accepted/published

1.      Regularity theory for parabolic equations with singular degenerate coefficients  (with H. Dong), Calculus of Variations and Partial Differential Equations, accepted, [arXiv].

2.      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, [Journal article]  [preprint].

3.      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,  accepted, arXiv:1811.06393 [arXiv].

4.      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]

5.      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]

6.      Well-posedness for the Navier-Stokes equations in critical mixed-norm Lebesgue spaces, Journal of Evolution Equations, 20(2020), 553-576 [Author shared link] [Journal article] [arXiv].

7.      Weighted Calderon-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations, Potential Analysis, 52 (2020), 393-425, DOI: 10.1007/s11118-018-9737-z  [Author shared link][Journal article], [arXiv].

8.      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].

9.      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].

10.    Lorentz estimates for weak solutions of quasi-linear parabolic equations with singular divergence-free   drifts, Canadian Journal of Mathematics, Vol 71, Issue 4 (2019), 937-982, [Journal version], [preprint]

Complete list of publication: list of publication and preprints

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

      Upcoming Events:   

1. Special Session on “Nonstandard elliptic and parabolic regularity theory with    applications”, AMS meeting Oct 10 -11, 2020, Chattanooga, TN

2. Conference of Analysis and Applied Mathematics, Sai Gon University, December 17 - 18, 2020, Ho Chi Minh City, Vietnam

CAAM’s information:    Conference on Analysis and Applied Mathematics.