Dissipative measure-valued solutions to the Euler-Poisson equation
<p>We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued solutions, i.e., very weak solutions descri...
| Asıl Yazarlar: | , , , |
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| Materyal Türü: | Journal article |
| Dil: | English |
| Baskı/Yayın Bilgisi: |
Society for Industrial and Applied Mathematics
2024
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| Özet: | <p>We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued solutions, i.e., very weak solutions described by a classical Young measure together with appropriate concentration defects. We then investigate the evolution of a relative energy functional to compare a measure-valued solution to a regular solution emanating from the same initial datum. This leads to a (partial) weak-strong uniqueness principle.</p> |
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