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Daily Overview |
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OT1: Optimal Transport: Theory and Applications Location: G227 Session Chair: Stephan Eckstein Session Chair: Johannes Wiesel | |
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Mass splitting in the generalized Euler equations and non-Monge solutions in multi-marginal optimal transport Technical University of Munich, Germany Brenier, building on earlier work by Arnold, introduced a celebrated variational formulation of the incompressible Euler equations of fluid dynamics. This formulation, after time discretization, is a prototype example of multi-marginal optimal transport, yet the question whether it exhibits mass-splitting (or equivalently, whether there exist solutions which are not of Monge form) has remained open. In this talk -- after introducing Arnold's and Brenier's formulations of Euler and explaining the connection to optimal transport -- we resolve this question by giving a mass-splitting example in one spatial dimension. Moreover we present a related and very simple fully discrete example of mass-splitting which reveals a transparent underlying mechanism. Reference: arXiv:2601.02616 (2026) | |
