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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.15886 |
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Table of Contents:
- We study the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a desired low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials, we can split the dynamics into the divergence-part and the curl-part, and each part satisfies a distinct coupled quasilinear wave system with respect to different acoustical metrics. Our main result is that the Sobolev norm $H^{3+}$ of the divergence-part (the faster-wave part) and the $H^{4+}$ of the curl-part (the slower-wave part) can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{3+}$ is optimal for the divergence-part. This marks the first favorable low-regularity local well-posedness result for a wave system with multiple wave speeds.