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<p>We introduce the concept of a dissipative measure-valued solution to the Euler alignment system. This approach incorporates a modified total energy balance, utilizing a binary tensor Young measure. The central finding is a weak (measure-valued)-strong uniqueness principle: if both a dissipative measure-valued solution and a classical smooth solution originate from the same initial data, they will be identical as long as the classical solution exists.</p>

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Dissipative measure-valued solutions and weak–strong uniqueness for the Euler alignment system

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月16日

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  • A. Chaudhary,
  • U. Koley,
  • E. Wiedemann

摘要

We introduce the concept of a dissipative measure-valued solution to the Euler alignment system. This approach incorporates a modified total energy balance, utilizing a binary tensor Young measure. The central finding is a weak (measure-valued)-strong uniqueness principle: if both a dissipative measure-valued solution and a classical smooth solution originate from the same initial data, they will be identical as long as the classical solution exists.