{
  "id": "2502.07521",
  "version": "v1",
  "published": "2025-02-11T12:52:44.000Z",
  "updated": "2025-02-11T12:52:44.000Z",
  "title": "The null condition in elastodynamics leads to non-uniqueness",
  "authors": [
    "Shunkai Mao",
    "Peng Qu"
  ],
  "comment": "68pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-11T12:52:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null condition",
      "non-uniqueness",
      "construct non-zero weak solutions",
      "convex integration techniques",
      "characteristic double wave speeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}