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arXiv · 2412.09590

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

Abhishek Chaudhary·Ujjwal Koley·Emil Wiedemann
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Abstract

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.

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Abhishek Chaudhary, Ujjwal Koley, Emil Wiedemann. 2024-12-12. Dissipative measure-valued solutions and weak-strong uniqueness for the Euler alignment system. https://arxiv.org/abs/2412.09590

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