Two-species system with nonlocal interactions driven by Riesz potentials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912995171368960 |
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| author | Fagioli, Simone Iorio, Valeria |
| author_facet | Fagioli, Simone Iorio, Valeria |
| contents | This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional orders. By exploiting optimal transportation theory and the theory of gradient flows in Wasserstein spaces, we establish the existence of weak solutions under singularity assumptions on all interaction potentials, provided the cross-interaction ones satisfy a symmetry condition. Our analysis extends previous results available for either single-species equations or multi-species systems with smoother cross-interaction kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00729 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-species system with nonlocal interactions driven by Riesz potentials Fagioli, Simone Iorio, Valeria Analysis of PDEs 35R11, 35A15, 35Q92, 45K05, 92C17 This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional orders. By exploiting optimal transportation theory and the theory of gradient flows in Wasserstein spaces, we establish the existence of weak solutions under singularity assumptions on all interaction potentials, provided the cross-interaction ones satisfy a symmetry condition. Our analysis extends previous results available for either single-species equations or multi-species systems with smoother cross-interaction kernels. |
| title | Two-species system with nonlocal interactions driven by Riesz potentials |
| topic | Analysis of PDEs 35R11, 35A15, 35Q92, 45K05, 92C17 |
| url | https://arxiv.org/abs/2604.00729 |