Hydrodynamic Stability and Bifurcation
Bifurcation Theory and Applications
Geometry and Topology of Incompressible Flows and Applications
Bifurcation Theory and Applications
The study in this area is on a new bifurcation theory developed recently by Ma and myself and its applications to various problems in science and engineering. The theory is based on a new notion of bifurcation called attractor bifurcation, together with new strategies of central manifold and Lyapunov-Schmidt reductions.
- Bifurcation theory and applications, World Scientific Series on Nonlinear Science, Series A - Vol. 53, World Scientific, Singapore 2005 (joint with Tian Ma)
- Attractor bifurcation of three dimensional double-diffusive
convection, submitted, 2005 (with C. Hsia and T. Ma)- Bifurcation and stability of two-dimensional double-diffusive
convection, submitted, 2005 (with C. Hsia and T. Ma)- Structure of Bifurcated Solutions of 2D Rayleigh-B\'enard Convection, submitted, 2005 (with Tian Ma)
- Dynamic Bifurcation and Stability of the Taylor Problem, Physica D, submitted, 2005 (with Tian Ma)
- Stability and bifurcation of the Taylor problem, Archive Rational Mechanics and Analysis, 2006 (with Tian Ma)
- Bifurcation and Stability of Superconductivity, Dedicated
to Professor Louis Nirenberg on the occasion of his eightieth birthday, Journal of Mathematical Physics, 46(2005) (with Tian Ma).- Dynamic bifurcation of nonlinear evolution equations,
Chinese Annals of Mathematics, 26:2(2005), 185-206 (with T. Ma).- Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation Methods and Applications of Analysis, 11:2(2004), 179-210
(with T. Ma).- Bifurcation of Nonlinear Equations: I. Steady State Bifurcation,
Methods and Applications of Analysis, 11:2(2004), 155-178
(with T. Ma).- Dynamic Bifurcation of the Ginzburg-Landau Equation, SIAM J. Applied Dynamics, 3:4(2004), 620-635 (with T. Ma and Jungho Park)
- Dynamic Bifurcation and Stability in the Rayleigh-B\'enard Convection, Communication in Math. Sci., 2:2(2004), 159-183 (with T. Ma)
- Hopf Bifurcation in Quasi-Geostrophic Channel Flow, SIAM J. Applied Math., 64:1(2004), 343-368 (with Z. Chen, M. Ghil and E. Simonnet)
- Attractor bifurcation theory and its applications to Rayleigh-B\'enard convection, Communications on Pure and Applied Analysis, 2:4(2003), 591--599 (with T. Ma)
The following papers are on numerical studies of shallow water models of the wind-driven ocean circulation.
- Low-Frequency Variability in Shallow Water Models of the
Wind-Driven Ocean Circulation. Part II: Time-Dependent Solutions, Journal of Physical Oceanography, 33(2003), 729-752 (with E. Simonnet, M. Ghil, K. Ide, and R. Temam).- Low-Frequency Variability in Shallow Water Models of
the Wind-Driven Ocean Circulation. Part I: Steady State Solutions, Journal of Physical Oceanography, 33(2003), 712-728 (with E. Simonnet, M. Ghil, K. Ide, and R. Temam)- Successive bifurcations in a shallow-water ocean model,
Dedicated to M. Holt on his 80th Birthday, in Sixteenth International Conference on Numerical Methods in Fluid Dynamics, Edited by Charles-Henri Bruneau, Lecture Notes
in Physics, Vol 515, Springer-Verlag, pp. 225-230, 1998
(with E. Simonnet, R. Temam, M. Ghil and K. Ide)