Mixed type PDEs and compressible flow
2013. 04. 11.
If density of flow is globally a constant, then the flow is said incompressible.
Otherwise, the flow is said compressible. Flow motion of compressible
inviscid flow is governed by Euler system. The Euler system is a nonlinear
PDE system describing conservation of mass, momentum and energy. Interestingly,
mathematical property of Euler system dramatically changes depending
on whether speed of flow exceeds sonic speed or not. In addition, nonlinearity
of Euler system can cause a shock or a contact discontinuity/vortex
sheet in which physical features of flow discontinuously change. This
talk will present mathematical approach to understand such nonlinear
physical phenomena. If time allows, some open problems will be discussed