A Moser-Type Construction for the Liouville Equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918403542876160 |
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| author | Borzì, Alfio Caponigro, Marco Vicari, Arianna |
| author_facet | Borzì, Alfio Caponigro, Marco Vicari, Arianna |
| contents | We present a novel extension of Moser's volume form lemma to the kinetic Liouville equation. In particular, we show that two smooth, positive phase-space densities $f$ and $g$ can be connected in unit time by the Liouville equation if and only if a natural compatibility condition on velocity marginals is satisfied. Under this condition, an explicit family of force fields is constructed via a weighted elliptic problem in the velocity variable. Results of numerical experiments are presented to validate the theoretical framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Moser-Type Construction for the Liouville Equation Borzì, Alfio Caponigro, Marco Vicari, Arianna Optimization and Control We present a novel extension of Moser's volume form lemma to the kinetic Liouville equation. In particular, we show that two smooth, positive phase-space densities $f$ and $g$ can be connected in unit time by the Liouville equation if and only if a natural compatibility condition on velocity marginals is satisfied. Under this condition, an explicit family of force fields is constructed via a weighted elliptic problem in the velocity variable. Results of numerical experiments are presented to validate the theoretical framework. |
| title | A Moser-Type Construction for the Liouville Equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.21850 |