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Bibliographic Details
Main Authors: Mao, Shunkai, Qu, Peng
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.07521
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Table of 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.