Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

Aneta Wr\'oblewska-Kami\'nska; Ewelina Zatorska; Jos\'e A. Carrillo

arxiv: 1906.00664 · v1 · pith:B2IC3UO5new · submitted 2019-06-03 · 🧮 math.AP

Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

Jos\'e A. Carrillo , Aneta Wr\'oblewska-Kami\'nska , Ewelina Zatorska This is my paper

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keywords navier-stokessystemdegenerateeulerpressurelesssolutionsartificialconfinement

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We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative entropy method using the artificial velocity formulation for the one-dimensional Navier-Stokes system.

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Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

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