| Abstract: |
| The main aim of this talk is to give a mathematical justification for the interactive boundary layer theory.
In the first part of the talk, we shall discuss the behavior of the Navier-Stokes solutions for a high Reynolds number flow interacting with a boundary.
To describe these flows, one usually introduces the boundary layer and the Prandtl equations.
A rigorous mathematical justification of this setting has been given in the analytic setting.
However, the Euler--Prandtl matching does not allow the interaction between the Boundary Layer and the outer flow:
this imposes severe limitations on the theory,
ultimately leading to the lack of a sound description of the transition phenomena occurring close to the boundary.
In the second part of the talk, we shall describe a different asymptotic approach that seems able to overcome the above-described difficulties. The well-posedness of the resulting equations in the analytic setting is the main result of the talk. |
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