Chongchun Zeng
Georgia Institute of Technology, GA·Mathematics & Statistics
Partial differential equations (PDEs) describe how quantities change across space and time, and they model problems in physics, engineering, biology and finance. Rigorous mathematical analysis of such models serves two purposes: comparing theory with experiments tests whether an idealized model is physically meaningful, and once a model is trusted, analysis can predict behavior that experiments struggle to reveal.
- Fields
Mathematics & Statistics
Physics
- Topics
partial differential equations
nonlinear waves
water waves
- Grants
- 1 known grant, through Jul 2027
What they work on
- Analyze two-dimensional water waves linearized at shear flows, where speed varies with depth, establishing the bifurcation of instability and linear inviscid damping for gravity water waves.
- Determine the spectra and linear flows of stratified water waves, in which fluid density varies in layers, near shear-flow steady states.
- Construct local invariant manifolds for quasilinear Hamiltonian partial differential equations despite the regularity obstacles, and study the unfolding bifurcation of small homoclinic-type solutions in a singular perturbation framework.
- Justify a potential flow approximation to weakly viscous water waves, first formally via multi-scale expansions involving boundary layers and then through rigorous proofs.
More about the research
For systems that evolve in time, special attention goes to structures such as equilibria and periodic, quasi-periodic or chaotic orbits, and to whether they are stable. Only stable states are normally observed, because unstable ones depend too sensitively on conditions. Unstable states still matter, since they and the structures attached to them form the boundaries between different families of stable behavior.
Why it matters
This is basic mathematical research on standard models of water waves, stratified fluids, atmosphere-ocean flows and nonlinear waves. Rigorous results on how stability and instability arise near steady states would clarify when these idealized models can be trusted and could reveal new physical and mathematical phenomena in the systems they describe.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Paul Carter
University of California-Irvine, CA·Mathematics & Statistics·Early-career
Analyze when bistable planar interfaces, boundaries between two stable states, become unstable and form patterns in multi-component reaction-diffusion systems, motivated by desertification fronts in drylands.
Zachary Bradshaw
University of Arkansas, AR·Mathematics & Statistics
Analyze the dynamic stability of multi-celled vortex solutions of the Navier-Stokes equations, such as tornado-like models with an updraft surrounding a central downdraft.
Dionyssios Mantzavinos
University of Kansas, KS·Mathematics & Statistics
Develop analytical tools to establish existence, uniqueness and stability of solutions to nonlinear partial differential equations posed in bounded domains in two or more spatial dimensions.
The school
Georgia Institute of Technology: 50 labs on PI Pages, $1.5B a year on research, 572 research doctorates a year.
Reach out
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