Non-uniqueness for the nonlinear dynamical Lamé system
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929709952008192 |
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| author | Mao, Shunkai Qu, Peng |
| author_facet | Mao, Shunkai Qu, Peng |
| contents | We consider the Cauchy problem for the nonlinear dynamical Lamé system with double wave speeds in a $d$-dimensional $(d=2,3)$ periodic domain. Moreover, the equations can be transformed into a linearly degenerate hyperbolic system. We could construct infinitely many continuous solutions in $C^{1,α}$ emanating from the same small initial data for $α<\frac{1}{60}$. The proof relies on the convex integration scheme. We construct a new class of building blocks with compression structure by using the double wave speeds characteristic of the equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness for the nonlinear dynamical Lamé system Mao, Shunkai Qu, Peng Analysis of PDEs We consider the Cauchy problem for the nonlinear dynamical Lamé system with double wave speeds in a $d$-dimensional $(d=2,3)$ periodic domain. Moreover, the equations can be transformed into a linearly degenerate hyperbolic system. We could construct infinitely many continuous solutions in $C^{1,α}$ emanating from the same small initial data for $α<\frac{1}{60}$. The proof relies on the convex integration scheme. We construct a new class of building blocks with compression structure by using the double wave speeds characteristic of the equations. |
| title | Non-uniqueness for the nonlinear dynamical Lamé system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.07385 |