Postdoctoral Research Associate

Department of Mathematics and Statistics

Texas Tech University

Box 41042

Lubbock, TX 79409-1042

Office: MA 205

Email: dat.cao [at] ttu [dot] edu

** Teaching **

- At Texas Tech University:
- Spring 2019: Math 3350-section 111: Higher Mathematics for Engineers and Scientists I
- Fall 2018: Math 3350-section 122: Higher Mathematics for Engineers and Scientists I
- Spring 2018: Math 2450-section 103: Calculus III with Applications
- Fall 2017: Math 2450-section 14: Calculus III with Applications
- Summer I 2017: Math 1452-section 102: Calculus II with Applications
- Spring 2017: Math 1452-section 102: Calculus II with Applications
- Fall 2016: Math 1451-section 16: Calculus I with Applications

- At University of Tennessee-Knoxville:
- Fall 2015, Spring 2016: Math 141: Calculus I (four sections)

- At University of Missouri-Columbia:
- Spring 2012, Spring 2015: Teaching assistant for Pre-Calculus (9 sections), Calculus I (6 sections)

** Research Interests **

- Partial Differential Equations, Nonlinear Potential Theory, Harmonic Analysis.

** Publications/Preprints **

- Dat Cao and Luan Hoang,
*Asymptotic expansions in a general system of decaying functions for solutions of the Navier-Stokes equations*, 54 pp, submitted, arXiv. - Dat Cao and Luan Hoang,
*Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces*,**Proc. Roy. Soc. Edinburgh Sect. A**, 38 pp, in press, DOI:10.1017/prm.2018.154 || arXiv. - Dat Cao, Tadele Mengesha, and Tuoc Phan,
*Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients,***AMS Contemporary Mathematics**, 21 pp, in press, preprint. - Dat Cao, Tadele Mengesha, and Tuoc Phan,
*Weighted W^{1,p} estimates for weak solutions of degenerate and singular elliptic equations,***Indiana Univ. Math. J.**, 67 No. 6 (2018), 2225-2277, journal article || arXiv. - Dat Cao, Akif Ibragimov, and Alexander I. Nazarov,
*Mixed boundary value problems for non-divergence type elliptic equations in unbounded domains,***Asymptot. Anal.**, 109 (2018), 75-90, journal article || arXiv. - Dat Cao and Igor Verbitsky,
*Nonlinear elliptic equations and intrinsic potentials of Wolff type,***J. Funct. Anal.,**272 (2017), 112-165, journal article || arXiv. - Dat Cao and Igor Verbitsky,
*Pointwise estimates of Brezis-Kamin type for solutions of sublinear elliptic equations,***Nonlinear Anal.,**146 (2016), 1-19, journal article || arXiv. - Dat Cao and Igor Verbitsky,
*Finite energy solutions of quasilinear elliptic equations with sub-natural growth terms,***Calc. Var. Partial Differential Equations,**52 (2015), 529-546, journal article || arXiv.

** Work in progress **

- Three asymptotic expansions for solutions of nonautonomous nonlinear differential equations, (with Luan Hoang), in preparation.
- Asymptotic expansions for solutions of ODEs, (with Luan Hoang and Thinh Kieu), in preparation.
- Regularity for degenerate/singular equations (with Tuoc Phan), in preparation.

** Conferences/Seminars **

- AMS 2019 Joint Mathematics Meetings, Baltimore, MD, January 16-19, 2019.
- SIAM Texas-Louisiana Section, Nonlinear partial differential equations and applications, Louisiana State University, October 5-7, 2018.
- AMS Spring Eastern Sectional Meeting, Special Session on Nonlinear and Stochastic Partial Differential Equations and Applications, Northeastern University, Boston, MA, April 21-22, 2018.
- AMS Spring Southeastern Sectional Meeting, Special Session on Evolution Equations and Applications, Vanderbilt University, Nashville, TN, April 14-15, 2018.
- The Eighth Ohio River Analysis Meeting, University of Kentucky, Lexington, Kentucky, March 24-25, 2018.
- Joint Analysis and Applied Math Seminar, Texas Tech University, November 8, 2017.
- AMS Fall Central Sectional Meeting, Special Session on Integrable Systems and Applications, University of North Texas, Denton, TX, September 9-10, 2017.
- Analysis Seminar, Texas Tech University, March 27 and April 5, 2017.
- AMS 2017 Joint Mathematics Meetings, Atlanta, GA, January 4-7, 2017.
- Applied Math Seminar, Texas Tech University, September 28, 2016.
- Colloquium, Department of Mathematics and Statistics, Texas Tech University, August 3, 2016.
- AMS Southeastern Sectional Meeting, Special Session on Sharp estimates and Bellman functions in Harmonic Analysis, University of Georgia in Athens, GA, March 5-6, 2016.
- The 35th Southeastern Atlantic Regional Conference on Differential Equations, University of North Carolina at Greensboro, October 10-11, 2015.
- Differential Equations Seminar, University of Tennessee, September 17 and 24, 2015.
- AMS Spring Southeastern Sectional Meeting, Special Session on Analysis on Nonlinear Integral and Partial Differential Equations, University of Alabama in Huntsville, March 27-29, 2015.
- The Fifth Ohio River Analysis Meeting, University of Cincinnati, Cincinnati, Ohio, February 28 - March 1, 2015.

** Collaborators: **
Luan Hoang, Akif Ibragimov, Tadele Mengesha, Alexander I. Nazarov, Tuoc Phan, Igor Verbitsky.

** Links: **