Math Park - 04/05/2014 - Laure Saint-Raymond, singularities of flows in shallow water

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Institut Henri Poincaré

Published on Streamed live on Apr 5, 2014
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The aim of this paper is to describe the qualitative behavior of the solutions of the Saint-Venant system governing the flow of a thin layer of incompressible fluid. For simplicity, we will in fact consider a scalar model that presents the same type of phenomenology, that is to say for which we observe in finite time the appearance of singularities corresponding to shocks. The propagation of shock waves can in fact be predicted by the same partial differential equation provided that we define a very weak notion of derivative. We will thus introduce in an elementary way the concept of distribution.

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