Lyonline Modeling, Analysis and Computing Seminar

Stability of the Prandtl System and the Zero Viscosity Limit

by Nader Masmoudi



The Prandtl system describe the flow of a viscous fluid close to the boundary. It was first derived by Prandtl in 1904. Since, then it had many applications in physics and mathematics. It particular it is a main model in the study  of flying objects and the design of airplanes. 
The model has a stationary version and a time evolution version. Both of therm are very physical and both of them are mathematically challenging: 
A/ The well posedness of the system requires a monotonicity condition or a very high regularity. 
B/ The stability of the model is still not well understood: The derivation of the model by studying the zero viscosity limit require a Gevrey regularity.