Mass splitting in the time-discrete generalized Euler equations and non-Monge solutions in multi-marginal optimal transport
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909982214062080 |
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| author | Friesecke, Gero |
| author_facet | Friesecke, Gero |
| contents | The time-discretized, spatially continuous generalized Euler equations are a prototype example of multi-marginal optimal transport, yet the question whether they exhibit mass-splitting (or equivalently, whether they have solutions that are not of Monge form) has remained open. Here 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_02616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mass splitting in the time-discrete generalized Euler equations and non-Monge solutions in multi-marginal optimal transport Friesecke, Gero Analysis of PDEs Optimization and Control 49Q22, 76B03 The time-discretized, spatially continuous generalized Euler equations are a prototype example of multi-marginal optimal transport, yet the question whether they exhibit mass-splitting (or equivalently, whether they have solutions that are not of Monge form) has remained open. Here 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. |
| title | Mass splitting in the time-discrete generalized Euler equations and non-Monge solutions in multi-marginal optimal transport |
| topic | Analysis of PDEs Optimization and Control 49Q22, 76B03 |
| url | https://arxiv.org/abs/2601.02616 |