Global Well-posedness for Incompressible Hookean Elastodynamics in the Critical Besov Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909320252227584 |
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| author | Zhang, Zexian Zhou, Yi |
| author_facet | Zhang, Zexian Zhou, Yi |
| contents | We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted $U^2$-type spaces to prove the small data global well-posedness in the critical Besov space $\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb{R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n)\ (n\ge 2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Well-posedness for Incompressible Hookean Elastodynamics in the Critical Besov Spaces Zhang, Zexian Zhou, Yi Analysis of PDEs We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted $U^2$-type spaces to prove the small data global well-posedness in the critical Besov space $\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb{R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n)\ (n\ge 2)$. |
| title | Global Well-posedness for Incompressible Hookean Elastodynamics in the Critical Besov Spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.19238 |