Welcome! Here are: a summary of my research interests and results;
a course pack that I developed for an undergraduate course on "Introduction to Numerical Methods".
- Short Curriculum Vitae (October, 2013)
- Research summary.
Fluid dynamics. Geophysical and astrophysical sciences. Singular limit problems in nonlinear PDEs. Numerical analysis and scientific computing. Kinetic formulation. Mathematical Physics in connection with these areas.
- Publications (move mouse over [...] to show abstract)
-  B. Cheng, Singular limits and convergence rates of compressible Euler and rotating shallow water equations. SIAM J. on Mathematical Analysis, vol. 44, pp. 1050-1076, 2012 (SIMA). Referee(s)' remarks. doi:10.1137/11085147X
-  B. Cheng and A. Mahalov, Euler equations on a fast rotating sphere --- time-averages and zonal flows. European J. Mech. - B/Fluids, vol. 37, pp. 48-58, 2013 (E.J.Mech.-B). doi:10.1016/j.euromechflu.2012.06.001
B. Cheng and A. Mahalov, Time averages of fast oscillatory systems. Discrete and Continuous Dynamical Systems - Series S, vol. 6, pp. 1151-1162 2013 (DCDS-S). doi:10.3934/dcdss.2013.6.1151
-  B. Cheng and C. Xie, On the classical solutions of two dimensional Rotating Shallow Water system. J. Differential Equations vol. 250, 690-709, 2011 (JDE). doi:10.1016/j.jde.2010.09.017
-  B. Cheng and E. Tadmor, Approximate periodic solutions for the rapidly rotating shallow-water and related equations. Water waves: theory and experiment -- Proc. of the conference, 69-78, World Scientific Pub. Co. Inc., 2010.
-  B. Cheng and E. Tadmor, An improved local blow-up condition for Euler-Poisson equations with attractive forcing, Physica D, vol. 238, pp. 2062-2066, 2009 (Phys. D). doi:10.1016/j.physd.2009.08.008
-  B. Cheng, Multiscale dynamics of 2D rotational compressible Euler equations. Hyperbolic problems: theory, numerics and applications, 497-506,
Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., 2009.
-  B. Cheng and E. Tadmor, Long time existence of smooth solutions for rapidly rotating shallow-water equations and Euler equations. SIAM J. on Mathematical Analysis, vol. 39, pp. 1668-1685, 2008 (SIMA). doi:10.1137/070693643
- Unpublished Work
2012 is Alan Turing Year
2013 is Year of Mathematics of Planet Earth