Hydrodynamic Stability and Bifurcation
Bifurcation Theory and Applications
Geometry and Topology of Incompressible Flows and Applications
Shouhong Wang
Professor
Department of Mathematics
Indiana University
Bloomington, IN 47405.
Books:
- Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics, AMS Monograph and Mathematical Survey Series, vol. 119, 2005 (with Tian Ma)
- Bifurcation Theory and Applications, World Scientific Series on Nonlinear Science, Series A - Vol. 53, 2005 (with Tian Ma)
- Phase Transition Dynamics in Nonlinear Sciences, in preparation (with T. Ma)
Recent Papers:
Equilibrium Phase Transitions:
- Phase Separation of Binary Systems (with T. Ma)
- Phase Transition and Separation for Mixture of Liquid He-3 and He-4, EJTP, a special issue dedicated to the Legacy of Landau (with Tian Ma)
- Cahn-Hilliard Equations and Phase Transition Dynamics for Binary Systems, DCDS-B (with T. Ma)
- Dynamic Transitions for PVT Systems, Indiana University Mathematics Journal, to appear (with T. Ma)
- Superfluidity of helium-3, Physica A, (with T. Ma)
- Dynamic Model and Phase Transitions for Liquid Helium, Journal of Mathematical Physics, 49:073304 (2008), 1-18 (with T. Ma)
- Dynamic Transitions for Ferromagnetism, Journal of Mathematical Physics, 49:053506 (2008), 1-18 (with T. Ma)
- Bifurcation and stability of superconductivity, J. Math. Phys., 46(2005), 095112 (with Ma) pdf file
Classical, Geophysical Fluid Dynamics and Climate Dynamics:
- Some mathematical and numerical issues in geophysical fluid dynamics and climate dynamics, Communications in Computational Physics, 2008 (with Jianping Li)
- Stratified Rotating Boussinesq Equations in Geophysical Fluid Dynamics: Dynamic Bifurcation and Periodic Solutions, J. Math. Phys., 48:065602 (2007), 1-20 (with Chun-Hsiung Hsia and Tian Ma) pdf file
- Attractor Bifurcation of Three-Dimensional Double-Diffusive Convection (with C. Hsia and T. Ma), ZAA (ArXiv, nlin.PS/0611024)
- Boundary Layer and Interior Separations in the Taylor--Couette--Poiseuille Flow (with T. Ma), Journal of Mathematical Physics, to appear (ArXiv, math-ph/0701073)
- Rayleigh-Benard Convection: Dynamics and Structure in the Physical Space, Comm. Math. Sci., 5:3(2007), 553-574 (with T. Ma) pdf file
- Stability and bifurcation of the Taylor problem, Archive Rational Mechanics and Analysis, 181:1(2006), 149-176 (with Tian Ma) pdf file
Spring 09 Teaching: