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arXiv · 1801.04683

The global Cauchy problem for compressible Euler equations with a nonlocal dissipation

Young-Pil Choi
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Abstract

This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic Cucker-Smale flocking equation with strong local alignment forces and diffusions through the hydrodynamic limit based on the relative entropy argument. In a perturbation framework, we establish the global existence of a unique strong solution for the system under suitable smallness and regularity assumptions on the initial data. We also provide the large-time behavior of solutions showing the fluid density and the velocity converge to its averages exponentially fast as time goes to infinity.

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Young-Pil Choi. 2018-01-15. The global Cauchy problem for compressible Euler equations with a nonlocal dissipation. https://arxiv.org/abs/1801.04683

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