Existence of weak solutions for fast diffusion equation with a divergence type of drift term
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917935495249920 |
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| author | Hwang, Sukjung Kang, Kyungkeun Kim, Hwa Kil |
| author_facet | Hwang, Sukjung Kang, Kyungkeun Kim, Hwa Kil |
| contents | We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term. Furthermore, in the case that the drift term has a divergence-free structure, it turns out that its integrability conditions can be relaxed, which is also applicable to porous medium equations, thereby improving previous results. As an application, the existence of weak solutions is also discussed for a viscous Boussinesq system of the fast diffusion type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of weak solutions for fast diffusion equation with a divergence type of drift term Hwang, Sukjung Kang, Kyungkeun Kim, Hwa Kil Analysis of PDEs 35A01, 35K55, 35K67 We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term. Furthermore, in the case that the drift term has a divergence-free structure, it turns out that its integrability conditions can be relaxed, which is also applicable to porous medium equations, thereby improving previous results. As an application, the existence of weak solutions is also discussed for a viscous Boussinesq system of the fast diffusion type. |
| title | Existence of weak solutions for fast diffusion equation with a divergence type of drift term |
| topic | Analysis of PDEs 35A01, 35K55, 35K67 |
| url | https://arxiv.org/abs/2501.09539 |