# The geometry of shock formation and maximal development for multi-D compressible Euler

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Special Princeton-Rutgers Analysis seminar
I will describe a new geometric framework for the multidimensional Euler equations, based on Arbitrary-Lagrangian-Eulerian (ALE) coordinates associated to fast'' characteristic surfaces. This framework is used to construct the maximal development of smooth Cauchy data for shock formation. The talk is based on a joint work with Steve Shkoller.