Stability of the Prandtl System and the Zero Viscosity Limit

par Nader Masmoudi

mardi 21 juin 2022, 14:30 → 15:30 Europe/Paris

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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.