Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914790071336960 |
|---|---|
| author | He, Siming |
| author_facet | He, Siming |
| contents | In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows He, Siming Analysis of PDEs In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection. |
| title | Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.06048 |