Hydrodynamic Stability and Bifurcation
Bifurcation Theory and Applications
Geometry and Topology of Incompressible Flows and Applications
Dynamical Systems
My study in dynamical systems (both finite dimensional and infinite dimensional) focuses in the following areas:
- dynamics of flow structures and their transitions in the physical spaces, described under the title: Geometry and Topology of Incompressible Flows and Applications
- bifurcation theory, described under the titles: Bifurcation Theory and Applications, and Hydrodynamic Stability and Bifurcation
- Long time dynamics of geophysical fluid dynamics models, and the Ginzburg-Landau equation of superconductivity.
- The following paper gives a simple way of proving the existence of global attractors for infinite dimensional systems:
- Necessary and Sufficient Conditions of Global Attractors of Semigroups and Applications (joint with Qingfeng Ma and Chengkui Zhong)