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arXiv · 2407.19238

Global Well-posedness for Incompressible Hookean Elastodynamics in the Critical Besov Spaces

Zexian Zhang·Yi Zhou
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Abstract

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 $\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb{R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n)\ (n\ge 2)$.

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Zexian Zhang, Yi Zhou. 2024-07-27. Global Well-posedness for Incompressible Hookean Elastodynamics in the Critical Besov Spaces. https://doi.org/10.1007/s00526-025-03075-6

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