Self-similarity in the singularity formation for the unsteady Prandtl’s equations and related problems

Collot, Charles

Séminaire Laurent Schwartz — EDP et applications (2017-2018), Exposé no. 18, 16 p.

The main issue of this text is the singularity formation problem for the two dimensional Prandtl’s system on the upper half plane, as well as for related models. The scaling invariance of the equation is partly responsible for the appearance of a self-similar phenomenon. It involves the formation of a shock along the tangential direction, together with an expansion along the transversal component due to incompressibility.

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