The classical theory of singular limits for evolutionary PDEs is mainly about the one parameter limit problem. But many physical systems contain several parameters such as the Mach number, Alfven number, Froude number, Rossby number, etc.. In order to determine the behavior of solution when two physical parameters tend to zero in a different manner, it is necessary to develop the theory for systems with three time scales.

I will discuss the recent developed theory for three scales singular limits of Evolutionary PDEs and its application to the singular limits for the compressible MHD equations.

This is a joint research work with Bin Cheng from University of Surrey and Steve Schochet from Tel-Aviv Univerisity.