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arxiv: 1611.07607 · v1 · pith:WP4K3HZNnew · submitted 2016-11-23 · 🧮 math.DS · math.AP

Inviscid limit for the compressible Euler system with non-local interactions

classification 🧮 math.DS math.AP
keywords systemeulercompressibleequationsdescribingsolutionsolutionsstrong
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The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of the compressible Euler equations with all of its unpleasant consequences, e.g., the non-uniqueness of solutions. In this paper, we analyze the equations describing a viscous approximation of a generalized compressible Euler system and we show that its dissipative measure-valued solutions tend to a strong solution of the Euler system as viscosity tends to 0, provided that the strong solution exists.

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