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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.07521 |
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| _version_ | 1866913686223847424 |
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| author | Mao, Shunkai Qu, Peng |
| author_facet | Mao, Shunkai Qu, Peng |
| contents | We consider the Cauchy problem for the system of elastodynamic equations in two dimensions. Specifically, we focus on materials characterized by a null condition imposed on the quadratic part of the nonlinearity. We can construct non-zero weak solutions $u \in C^1([0, T] \times \mathbb{T}^2)$ that emanate from zero initial data. The proof relies on the convex integration scheme. By exploiting the characteristic double wave speeds of the equations, we construct a new class of building blocks. This work extends the application of convex integration techniques to hyperbolic systems with a null condition and reveals the rich solution structure in nonlinear elastodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The null condition in elastodynamics leads to non-uniqueness Mao, Shunkai Qu, Peng Analysis of PDEs We consider the Cauchy problem for the system of elastodynamic equations in two dimensions. Specifically, we focus on materials characterized by a null condition imposed on the quadratic part of the nonlinearity. We can construct non-zero weak solutions $u \in C^1([0, T] \times \mathbb{T}^2)$ that emanate from zero initial data. The proof relies on the convex integration scheme. By exploiting the characteristic double wave speeds of the equations, we construct a new class of building blocks. This work extends the application of convex integration techniques to hyperbolic systems with a null condition and reveals the rich solution structure in nonlinear elastodynamics. |
| title | The null condition in elastodynamics leads to non-uniqueness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.07521 |