Relative entropy method for the relaxation limit of hydrodynamic models
We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We discuss the assumptions on the confinement and interaction...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Institute of Mathematical Sciences
2020
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| _version_ | 1797054941228957696 |
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| author | Carrillo de la Plata, J Peng, Y Wróblewska-Kamińksa, A |
| author_facet | Carrillo de la Plata, J Peng, Y Wróblewska-Kamińksa, A |
| author_sort | Carrillo de la Plata, J |
| collection | OXFORD |
| description | We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We discuss the assumptions on the confinement and interaction potentials depending on the relative energy of the free energy functional allowing for this relaxation limit to hold. We deal with weak solutions for the nonlocal compressible Euler-type systems and strong solutions for the limiting aggregation-diffusion equations. Finally, we show the existence of weak solutions to the nonlocal compressible Euler-type systems satisfying the needed properties for completeness sake. |
| first_indexed | 2024-03-06T19:04:24Z |
| format | Journal article |
| id | oxford-uuid:14a41b62-b58b-4dde-b6b0-897836525633 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:04:24Z |
| publishDate | 2020 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:14a41b62-b58b-4dde-b6b0-8978365256332022-03-26T10:21:07ZRelative entropy method for the relaxation limit of hydrodynamic modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:14a41b62-b58b-4dde-b6b0-897836525633EnglishSymplectic ElementsAmerican Institute of Mathematical Sciences2020Carrillo de la Plata, JPeng, YWróblewska-Kamińksa, AWe show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We discuss the assumptions on the confinement and interaction potentials depending on the relative energy of the free energy functional allowing for this relaxation limit to hold. We deal with weak solutions for the nonlocal compressible Euler-type systems and strong solutions for the limiting aggregation-diffusion equations. Finally, we show the existence of weak solutions to the nonlocal compressible Euler-type systems satisfying the needed properties for completeness sake. |
| spellingShingle | Carrillo de la Plata, J Peng, Y Wróblewska-Kamińksa, A Relative entropy method for the relaxation limit of hydrodynamic models |
| title | Relative entropy method for the relaxation limit of hydrodynamic models |
| title_full | Relative entropy method for the relaxation limit of hydrodynamic models |
| title_fullStr | Relative entropy method for the relaxation limit of hydrodynamic models |
| title_full_unstemmed | Relative entropy method for the relaxation limit of hydrodynamic models |
| title_short | Relative entropy method for the relaxation limit of hydrodynamic models |
| title_sort | relative entropy method for the relaxation limit of hydrodynamic models |
| work_keys_str_mv | AT carrillodelaplataj relativeentropymethodfortherelaxationlimitofhydrodynamicmodels AT pengy relativeentropymethodfortherelaxationlimitofhydrodynamicmodels AT wroblewskakaminksaa relativeentropymethodfortherelaxationlimitofhydrodynamicmodels |