Non-uniqueness for the nonlinear dynamical Lamé system

Fuente: arXiv
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Autores principales: Mao, Shunkai, Qu, Peng
Formato: Preprint
Publicado: 2025
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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