Incompressible limit for the compressible viscoelastic fluids in critical space
In this article, we consider the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the compressible viscoelastic fluids in the sense of critical Besov framework. We decouple our compressible system into two coupling sub-systems by introducing a skew sy...
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De Gruyter
2025-01-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2024-0062 |
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| author | Han Bin Wu Dan |
| author_facet | Han Bin Wu Dan |
| author_sort | Han Bin |
| collection | DOAJ |
| description | In this article, we consider the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the compressible viscoelastic fluids in the sense of critical Besov framework. We decouple our compressible system into two coupling sub-systems by introducing a skew symmetric matrix, which is related to the deformation tensor. This work generalizes the similar result obtained by Hu et al. (Incompressible limit for compressible viscoelastic flows with large velocity, Advances in Nonlinear Analysis 12 (2023), 20220324) to the critical functional space with respective to the natural scaling of the system. The proof relies on the dispersive property of the linear system on the high-frequency regime and the parabolic property on the low-frequency regime. The dispersion tends to disappear when λ\lambda tends to infinite, but having large λ\lambda provides strong dissipation on the potential part of the velocity and thus makes the flow almost incompressible. In addition, by exploiting the intrinsic structure of the viscoelastic system, we obtain the global uniform estimates of the solutions near equilibrium. |
| format | Article |
| id | doaj-art-68fbf2f65cbb4993a99c15dc2ed40306 |
| institution | Kabale University |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-68fbf2f65cbb4993a99c15dc2ed403062025-02-02T15:44:37ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-01-011415313610.1515/anona-2024-0062Incompressible limit for the compressible viscoelastic fluids in critical spaceHan Bin0Wu Dan1School of Mathematics and Statistics, Donghua University, Shanghai, 201620, P. R. ChinaSchool of Mathematical Sciences, Hangzhou Dianzi University, Hangzhou, 310018, P. R. ChinaIn this article, we consider the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the compressible viscoelastic fluids in the sense of critical Besov framework. We decouple our compressible system into two coupling sub-systems by introducing a skew symmetric matrix, which is related to the deformation tensor. This work generalizes the similar result obtained by Hu et al. (Incompressible limit for compressible viscoelastic flows with large velocity, Advances in Nonlinear Analysis 12 (2023), 20220324) to the critical functional space with respective to the natural scaling of the system. The proof relies on the dispersive property of the linear system on the high-frequency regime and the parabolic property on the low-frequency regime. The dispersion tends to disappear when λ\lambda tends to infinite, but having large λ\lambda provides strong dissipation on the potential part of the velocity and thus makes the flow almost incompressible. In addition, by exploiting the intrinsic structure of the viscoelastic system, we obtain the global uniform estimates of the solutions near equilibrium.https://doi.org/10.1515/anona-2024-0062compressible viscoelastic fluidsincompressible limitcritical regularity35a0576a1076d03 |
| spellingShingle | Han Bin Wu Dan Incompressible limit for the compressible viscoelastic fluids in critical space Advances in Nonlinear Analysis compressible viscoelastic fluids incompressible limit critical regularity 35a05 76a10 76d03 |
| title | Incompressible limit for the compressible viscoelastic fluids in critical space |
| title_full | Incompressible limit for the compressible viscoelastic fluids in critical space |
| title_fullStr | Incompressible limit for the compressible viscoelastic fluids in critical space |
| title_full_unstemmed | Incompressible limit for the compressible viscoelastic fluids in critical space |
| title_short | Incompressible limit for the compressible viscoelastic fluids in critical space |
| title_sort | incompressible limit for the compressible viscoelastic fluids in critical space |
| topic | compressible viscoelastic fluids incompressible limit critical regularity 35a05 76a10 76d03 |
| url | https://doi.org/10.1515/anona-2024-0062 |
| work_keys_str_mv | AT hanbin incompressiblelimitforthecompressibleviscoelasticfluidsincriticalspace AT wudan incompressiblelimitforthecompressibleviscoelasticfluidsincriticalspace |