Department of Mathematics and Statistics

Florida International University

Miami, Florida

I obtained my PhD in mathematics from the University of Nebraska-Lincoln in 2012, and my thesis advisor was Mohammad A. Rammaha. From 2012 to 2015, I was a postdoctoral fellow working with Edriss S. Titi, at the Weizmann Institute of Science in Israel. During the 2015-2016 school year, I was a lecturer at Texas A&M University. Currently, I am an Assistant Professor at Florida International University.

** Research Interest: ** Analysis of evolutionary partial differential equations for fluid or nonlinear waves.

** Grant: ** Simons collaboration grant (2017-2022)

** Papers: **

17. Global well-posedness for nonlinear wave equations with supercritical source and damping terms, J. Math. Anal. Appl. 477 (2019), 1087-1113.
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16. Global regularity for a rapidly rotating constrained convection model of tall columnar structure with weak dissipation, (with C. Cao and E. S. Titi), submitted. arXiv:1810.03596
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15. Global strong solutions for the three-dimensional Hasegawa-Mima model with partial dissipation, (with C. Cao and E. S. Titi), J. Math. Phys. 59, 071503 (2018). PDF

14. Energy decay of a viscoelastic wave equation with supercritical nonlinearities, (with M. A. Rammaha and S. Sakuntasathien), Z. Angew.
Math. Phys. (2018). PDF

13. Inertial manifolds for the hyperviscous Navier-Stokes equations, (with C. G. Gal), J. Differential Equations 265 (2018), 4335-4374. PDF

12. Blow-up of a hyperbolic equation of viscoelasticity with
supercritical nonlinearities, (with M. A. Rammaha and S.
Sakuntasathien), J. Differential Equations 262 (2017), 1956-1979. PDF

11. Non-viscous regularization of the Davey-Stewartson equations:
Analysis and modulation theory, (with I. Hacinliyan and E. S. Titi), J.
Math. Phys. 57 (2016), 081502, 22 pp. PDF

10. On the backward behavior of some dissipative evolution equations, (with E. S. Titi), Physica D 306 (2015), 34-47. PDF

9. Inertial manifolds for certain sub-grid scale alpha-models of
turbulence, (with M. Abu Hamed and E. S. Titi), SIAM J. Appl. Dyn. Syst. 14 (2015), 1308-1325. PDF

8. Global well-posedness of a system of nonlinearly coupled KdV
equations of Majda and Biello, (with K. Simon and E. S. Titi),
Commun. Math. Sci. 13 (2015), 1261-1288. PDF

7. On the radius of analyticity of solutions to the cubic Szego
equation, (with P. Gerard and E. S. Titi), Ann. Inst. H. Poincare Anal.
Non Lineaire 32 (2015), 97-108. PDF

6. Hadamard well-posedness for a hyperbolic equation of viscoelasticity
with supercritical sources and damping, (with M. A. Rammaha, S.
Sakuntasathien, E. S. Titi, and D. Toundykov), J. Differential
Equations 257 (2014), 3778-3812. PDF

5. Systems of nonlinear wave equations with damping and supercritical
interior and boundary sources, (with M. A. Rammaha), Trans. Amer. Math.
Soc. 366 (2014), 2265-2325. PDF

4. Persistency of analyticity for nonlinear wave equations: an
energy-like approach, (with E. S. Titi), Bull. Inst. Math. Acad. Sin.
(N.S.) 8 (2013), 445-479. (special issue dedicated to Neil Trudinger on
the occasion of his
70th birthday) PDF

3. Global existence and decay of energy to systems of wave equations
with damping and supercritical sources, (with M. A. Rammaha), Z. Angew.
Math. Phys. 64 (2013), 621-658. PDF

2. Blow-up of solutions to systems of nonlinear wave equations with
supercritical sources, (with M. A. Rammaha), Appl. Anal. 92 (2013),
1101-1115. PDF

1. Convex integrals on Sobolev spaces, (with V. Barbu, M. A. Rammaha, and D. Toundykov), J. Convex Anal. 19 (2012), 837-852. PDF