Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the probl...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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De Gruyter Open
2021
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| _version_ | 1826303289980878848 |
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| author | Carrillo de la Plata, JA Lin, K |
| author_facet | Carrillo de la Plata, JA Lin, K |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species. |
| first_indexed | 2024-03-07T06:00:24Z |
| format | Journal article |
| id | oxford-uuid:ebfe788f-3908-48ff-bc3b-e9274e757f76 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:00:24Z |
| publishDate | 2021 |
| publisher | De Gruyter Open |
| record_format | dspace |
| spelling | oxford-uuid:ebfe788f-3908-48ff-bc3b-e9274e757f762022-03-27T11:14:07ZSharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction systemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ebfe788f-3908-48ff-bc3b-e9274e757f76EnglishSymplectic ElementsDe Gruyter Open2021Carrillo de la Plata, JALin, KWe consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species. |
| spellingShingle | Carrillo de la Plata, JA Lin, K Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_full | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_fullStr | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_full_unstemmed | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_short | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_sort | sharp conditions on global existence and blow up in a degenerate two species and cross attraction system |
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