Office: DM 414C
Email: yanguo@fiu.edu
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 2015-2016, I was a lecturer at Texas
A&M University. Currently, I am an Associate Professor at Florida
International University.
Research Interests: My primary focus lies in the analysis of nonlinear partial differential equations, with a particular emphasis on the Navier-Stokes equations and nonlinear wave equations. I explore various aspects, including well-posedness, regularity, finite-time blow-up phenomena, and the long-term behavior of solutions. Additionally, I have an interest in number theory and its applications to PDEs.
Papers:
24. Exploring large-time dynamics: rapidly rotating convection model at infinite Prandtl number, (with J. Tian), submitted (2024).
23. Inertial manifolds for the two-dimensional hyperviscous Navier-Stokes equations, arXiv:2401.14642 [math.AP] (2024) PDF
22. Sparse distribution of lattice points in annular
regions, (with M. Ilyin), arXiv:2309.10971 [math.NT] (2023) PDF
21. Analysis of a rapidly rotating convection model without thermal diffusion, (with Cao and Titi), preprint (2023)
20. Blow-up theorems for a structural acoustics model, (with B. Feng and M. A. Rammaha), J. Math. Anal. Appl. 529 (2024), Paper No. 127600, 26 pp. PDF
19. On the asymptotic behavior of solutions to a structural acoustics model, (with B. Feng and M. A. Rammaha), J. Differential Equations 372 (2023), 315-347. PDF
18. Global well-posedness
for a rapidly rotating convection model of tall columnar structure in the limit
of infinite Prandtl number, (with C. Cao and E. S. Titi), J. Evol. Equ. 21 (2021), 2923-2954. PDF
17. Global regularity for a rapidly rotating constrained
convection model of tall columnar structure with weak dissipation, (with C. Cao
and E. S. Titi), J. Differential Equations 269 (2020), 8736-8769. PDF
16. Global well-posedness for
nonlinear wave equations with supercritical source and damping terms, J. Math.
Anal. Appl. 477 (2019), 1087-1113. PDF
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 (2018), 071503, 12 pp. PDF
14. Energy decay of a viscoelastic wave equation with
supercritical nonlinearities, (with M. A. Rammaha and
S. Sakuntasathien), Z. Angew.
Math. Phys. 69 (2018), Paper No. 65, 28 pp. 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