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 

1. 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.)
2. Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., 52(1999), 983-1046 (with P. Bates and K. Lu).
3. Homoclinic orbits for perturbed sine-Gordon equation, Comm. Pure. Appl. Math., 53(2000), 283-299 (with J. Shatah). 
4. Invariant foliations near a normally hyperbolic invariant manifold for semiflows, Trans. Amer. Math. Soc., 352 (2000), 4641-4676 (with P. Bates and K. Lu). 
5. Homoclinic orbits for perturbed nonlinear Shroedinger equation, Comm. Pure. Appl. Math., 53(2000), 1222-1283. (Erratum: Comm. Pure. Appl. Math., 53(2000), 1603-1605.) 
6. Periodic solutions for Hamiltonian Systems under strong constraining forces, J. Diff. Equa., 186(2002), 572-585 (with J. Shatah). 
7. Orbits homoclinic to center manifolds of conservative PDEs, 24pp, Nonlinearity, 16(2003), 591--614 (with J. Shatah). 
8. Constrained wave equations and wave maps, Comm. Math. Phys., 239 (2003), 383-404 (with J. Shatah). 
9. Schrodinger Maps and Anti-ferromagnetic Chains, Comm. Math. Phys.,262 (2006), 299-315 (with J. Shatah)
10. Schroedinger Maps and their associated Frame Systems, IMRN, 2007 (2007) (with A. Nahmod, L. Vega, and J. Shatah). 
11. 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) 
12. A priori estimates for fluid Interface problems, Comm. Pure. Appl. Math., 61 (2008), 848--876 (With J. Shatah).
13. Approximately invariant manifolds and global dynamics of spike states, Inventiones Mathematicae, 174 (2008), 355--433. (With P. Bates and K. Lu.)
14. Self-similar Solutions of Schr\"{o}dinger Flows, Calc. Var. Partial Differential Equations34 (2009), 267--277. (With W. Ding and H. Tang.)
15. Self-similar Solutions for the Schr\"{o}dinger map equation, Math. Z.  264(2010), no. 3, 697--707. (With P. Germain and J. Shatah.)
16. Local well-posedness for the fluid interface problems, to appear in Arch. Ration. Mech. Anal. 199 (2011), no. 2, 653–705,.(With J. Shatah.) 
17. Normally elliptic singular perturbations and persistence of homoclinic orbits. J. Diff. Equa., 250 (2011), no. 11, 4124–4176. (With N. Lu.)
18. 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.)
19. Small BGK Waves and Nonlinear Landau Damping, Comm. Math. Phys., 306 (2011) no. 2, 291--331. (with Z. Lin.)
20. Inviscid Dynamical Structures Near Couette Flow,  Arch. Ration. Mech. Anal., 200 (2011) no. 3, 1075--1097. (with Z. Lin.)
21. Small BGK waves and nonlinear Landau damping (higher dimensions), Indiana Univ. Math. J., 61 (2012), no. 5, 1711–1735. (With Z. Lin.)
22. Absolute continuity of stable foliations for infinite dimensional systems, J. Diff. Equa., 254 (2013), no. 1, 283–308.(With L-S. Young and Z. Lian.)
23. Travelling water waves with compactly supported vorticity. Nonlinearity26 (2013), no. 6, 1529–1564. (With J. Shatah and S. Walsh)
24. 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.)  
25. 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)
26. 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)
27. 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)
28. Solutions of the generalized Lennard-Jones system. Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 2, 139–170. (With B. Liu and Y. Long)
29. 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)
30. 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)
31. 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)
32. Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs, Mem. Amer. Math. Soc., 275 (2022), no. 1347, 146 pages. (With Z. Lin)
33. 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.)
    
34. 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)
35. 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.)
36.  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.)
37. 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.)

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