**Curriculum Vitae**

**Chongchun Zeng**

**Education**

- January
1994-August 1997: Brigham Young Univ., Ph.D. in Mathematics

Advisor: Prof. Peter W. Bates

Thesis: Normally hyperbolic invariant manifolds and foliations for semiflows in Banach spaces - September
1990-November 1993: Nankai Univ., Tianjin, P. R. China; Undergraduate
in Mathematics

**Professional Experience**

- September 2009 --
present: Professor, School of Math., Georgia
Institute of Technology
- September 2005 --
August 2009: Associate Professor, School of Math., Georgia Institute
of Technology
- September 2000 --
August 2005: Assistant Professor, Dept. of Math., University of
Virginia
- September 1997 --
August 2000: Courant Instructor, Courant Institute of Math. Sci., New
York University

**Research Grants and Awards**

- AMS
fellow, class of 2019.
- Dynamics of Fluid and Nonlinear Waves, NSF DMS 19000083, 2019-2022.
- Dynamics of inviscid fluids and nonlinear waves, NSF DMS 1362507, 2014-2017.
- The Isentropic Euler Equations and Optimal Transport, NSF DMS 1101423, 2011-2014.
- Interface problems in fluids and nonlinear waves. NSF DMS 0801319, 2008-2011.
- Sloan Fellowship: 2004.
- Career Award: Career: Perturbation problems in PDE Dynamics. NSF DMS Analysis 0627842 (formerly 0239389), 2003-2008.
- Hamiltonian motions under strong constraints. NSF DMS Analysis, 0101969, 2001-2004.
- Dynamics of Weak Diffusive PDEs, New York University Research Challenge Fund, 1999. (The proposal was externally reviewed.)

**Research Interests** : Applied dynamical
systems and nonlinear PDEs

- Regularity and
dynamics of nonlinear PDEs, such as well-posedness, stability/instability, and
invariant structures (periodic/quasi-periodic/homoclinic/heteroclinic
solutions, traveling waves,
*etc.*) of nonlinear wave type equations, nonlinear Schr\"odinger type equations, fluid equations (including free boundary problems such water waves),*etc*.

- General theory of
infinite dimensional dynamical systems, including persistence,
smoothness, and dynamics in neighborhoods, of invariant manifolds and
foliations for semiflows, approximate invariant manifolds and their
applications to PDE singular perturbations problems.

**Selected Publications**

- Existence and
Persistence of Invariant Manifolds for Semiflows in Banach Spaces,
*Mem. Amer. Math. Soc.*,**645**(1998), 129 pp. (with P. Bates and K. Lu). (This paper received a FEATURED REVIEW from Math. Review.) - Persistence of
overflowing manifolds for semiflow,
*Comm. Pure Appl. Math.*,**52**(1999), 983-1046 (with P. Bates and K. Lu). - Homoclinic orbits
for perturbed sine-Gordon equation,
*Comm. Pure. Appl. Math.*,**53**(2000), 283-299 (with J. Shatah). - Invariant
foliations near a normally hyperbolic invariant manifold for
semiflows,
*Trans. Amer. Math. Soc.*,**352**(2000), 4641-4676 (with P. Bates and K. Lu). - Homoclinic orbits
for perturbed nonlinear Shroedinger equation,
*Comm. Pure. Appl. Math.*,**53**(2000), 1222-1283. (Erratum:*Comm. Pure. Appl. Math.*,**53**(2000), 1603-1605.) - Periodic
solutions for Hamiltonian Systems under strong constraining forces,
*J. Diff. Equa.*,**186**(2002), 572-585 (with J. Shatah). - Orbits homoclinic
to center manifolds of conservative PDEs, 24pp,
*Nonlinearity*,**16**(2003), 591--614 (with J. Shatah). - Constrained wave
equations and wave maps,
*Comm. Math. Phys.*,**239**(2003), 383-404 (with J. Shatah). - Schrodinger Maps
and Anti-ferromagnetic Chains,
*Comm. Math. Phys.,***262**(2006)**,**299-315 (with J. Shatah) - Schroedinger Maps
and their associated Frame Systems,
*IMRN,***2007**(2007) (with A. Nahmod, L. Vega, and J. Shatah). - Geometry and a
priori estimates for free boundary problems of the Euler's equation,
*Comm. Pure. Appl. Math.,***61**(2008), 698--744. (With J. Shatah) - A priori
estimates for fluid Interface problems,
*Comm. Pure. Appl. Math.,***61**(2008), 848--876 (With J. Shatah). - Approximately
invariant manifolds and global dynamics of spike states,
*Inventiones Mathematicae*,**174**(2008), 355--433. (With P. Bates and K. Lu.) - Self-similar
Solutions of Schr\"{o}dinger Flows,
*Calc. Var. Partial Differential Equations***34**(2009), 267--277. (With W. Ding and H. Tang.) - Self-similar
Solutions for the Schr\"{o}dinger map equation,
*Math. Z.***264**(2010), no. 3, 697--707. (With P. Germain and J. Shatah.) - Local
well-posedness for the fluid interface problems, to appear in
*Arch. Ration. Mech. Anal.*199 (2011), no. 2, 653–705,.(With J. Shatah.) - Normally elliptic
singular perturbations and persistence of homoclinic orbits.
*J. Diff. Equa.*, 250 (2011), no. 11, 4124–4176. (With N. Lu.) - Radial standing
and self-similar waves for the hyperbolic cubic NLS in 2D.
*Nonlinearity*24 (2011), no. 5, 1523–1538. (with P. Kevrekidis and A. Nahmod.) - Small BGK Waves
and Nonlinear Landau Damping,
*Comm. Math. Phys*., 306 (2011) no. 2, 291--331. (with Z. Lin.) - Inviscid
Dynamical Structures Near Couette Flow,
*Arch. Ration. Mech. Anal., 200 (2011)*no. 3, 1075--1097. (with Z. Lin.) - Small BGK waves
and nonlinear Landau damping (higher dimensions),
*Indiana Univ. Math. J.*, 61 (2012), no. 5, 1711–1735. (With Z. Lin.) - Absolute
continuity of stable foliations for infinite dimensional systems
*, J. Diff. Equa.*,*.*(With L-S. Young and Z. Lian.) - Travelling water
waves with compactly supported vorticity.
*Nonlinearity*26 (2013), no. 6, 1529–1564. (With J. Shatah and S. Walsh) - Unstable
manifolds of Euler equation,
*Comm. Pure. Appl. Math.*, 66 (2013), no. 11, 1803–1836. (With Z. Lin.) (Corrigendum:*Comm. Pure. Appl. Math.*, 67 (2014), no. 7, 1215–1217.) - Equivariante and
Self-similar Standing Waves for a Hamiltonian Hyperbolic-hyperbolic
Spin-field System,
*SIAM J. Math. Anal.*46-6 (2014), pp. 3913-3956. (N. Lu and A. Nahmod) - Stability of
Traveling Waves of Nonlinear Schrödinger Equation with Nonzero
Condition at Infinity,
*Arch. Ration. Mech. Anal.*222 (2016), no. 1, 143–212. (With Z. Lin nad Z. Wang) - On the Wind
Generation of Water Waves,
*Arch. Ration. Mech. Anal.*, 222 (2016), no. 2, 827--878. (With O. Buhler, J. Shatah, and S. Walsh) - Solutions of the
generalized Lennard-Jones system.
*Acta Math. Sin. (Engl. Ser.)*34 (2018), no. 2, 139–170. (With B. Liu and Y. Long) - Invariant
Manifolds of Traveling Waves of the 3D Gross–Pitaevskii Equation in
the Energy Space.
*Comm. Math. Phys.*364 (2018), no. 3, 981–1039. (With J. Jin and Z. Lin) - Concentrated steady vorticities of the
Euler equation on 2-d domains and their linear stability,
*J. Diff. Equa.*, 266 (2019), no. 10, 6661–6701. (With Y. Long and Y. Wang) - Dynamics near the solitary waves of the
supercritical gKDV equations,
*J. Diff. Equa.*, 267 (2019), no. 12, 7213--7262. (With J. Jin and Z. Lin) - Instability, index theorem, and
exponential trichotomy for Linear Hamiltonian PDEs,
*Mem. Amer. Math. Soc.*, 275 (2022), no. 1347, 146 pages. (With Z. Lin) - Dynamics of threshold solutions for energy critical NLS
with inverse square potential,
*SIAM J. Math. Anal.*, 54 (2022), no. 1, 173-219. (With Kai Yang and Xiaoyi Zhang.) - Smooth stationary water waves with exponentially localized
vorticity,
*J. Eur. Math. Soc.*(JEMS), 25 (2023), no. 3 , 1045–1090. https://arxiv.org/abs/1907.07335. (With M. Ehrnstrom and S. Walsh) - Separable Hamiltonian PDEs and Turning
point principle for stability of gaseous stars,
*Comm. Pure. Appl. Math.*, 75 (2022), no. 11, 2511–2572. http://arxiv.org/abs/2005.00973. (With Z. Lin.) - Asymptotic simplification of aggregation-diffusion equations towards the heat kernel,
*Arch. Ration. Mech. Anal.**,*247 (2023), no. 1, Paper No. 11, 45 pp. (With J. A. Carrillo, D. Gomez-Castro, Y. Yao.) - Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping,
*Mem. Amer. Math. Soc.*, accepted, 96 pages. https://arxiv.org/abs/2110.12604. (With X. Liu.)