Weak solutions for Euler systems with non-local interactions
We consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2, 3. These models arise in the study of self-organization in collective behavior modeling...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2017
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| _version_ | 1797065617254121472 |
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| author | Carrillo De La Plata, J Feireisl, E Gwiazda, P Swierczewska-Gwiazda, A |
| author_facet | Carrillo De La Plata, J Feireisl, E Gwiazda, P Swierczewska-Gwiazda, A |
| author_sort | Carrillo De La Plata, J |
| collection | OXFORD |
| description | We consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2, 3. These models arise in the study of self-organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-Time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality).We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure-driven Euler system with non-local interaction terms as well as for the pressurelesssystem with Newtonian interaction. |
| first_indexed | 2024-03-06T21:31:12Z |
| format | Journal article |
| id | oxford-uuid:44bc74c1-6b0d-433a-a01e-6a0f1e4499ad |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:31:12Z |
| publishDate | 2017 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:44bc74c1-6b0d-433a-a01e-6a0f1e4499ad2022-03-26T15:03:33ZWeak solutions for Euler systems with non-local interactionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:44bc74c1-6b0d-433a-a01e-6a0f1e4499adEnglishSymplectic ElementsWiley2017Carrillo De La Plata, JFeireisl, EGwiazda, PSwierczewska-Gwiazda, AWe consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2, 3. These models arise in the study of self-organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-Time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality).We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure-driven Euler system with non-local interaction terms as well as for the pressurelesssystem with Newtonian interaction. |
| spellingShingle | Carrillo De La Plata, J Feireisl, E Gwiazda, P Swierczewska-Gwiazda, A Weak solutions for Euler systems with non-local interactions |
| title | Weak solutions for Euler systems with non-local interactions |
| title_full | Weak solutions for Euler systems with non-local interactions |
| title_fullStr | Weak solutions for Euler systems with non-local interactions |
| title_full_unstemmed | Weak solutions for Euler systems with non-local interactions |
| title_short | Weak solutions for Euler systems with non-local interactions |
| title_sort | weak solutions for euler systems with non local interactions |
| work_keys_str_mv | AT carrillodelaplataj weaksolutionsforeulersystemswithnonlocalinteractions AT feireisle weaksolutionsforeulersystemswithnonlocalinteractions AT gwiazdap weaksolutionsforeulersystemswithnonlocalinteractions AT swierczewskagwiazdaa weaksolutionsforeulersystemswithnonlocalinteractions |