Recent results on the singular local limit for nonlocal conservation laws

2019/02/19 by Maria Colombo, Gianluca Crippa, Colombo, Maria +5 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1902.06970

openalex publication_date 2019/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an informal overview of recent developments concerning the singular local limit of nonlocal conservation laws. In particular, we discuss some counterexamples to convergence and we highlight the role of numerical viscosity in the numerical investigation of the nonlocal-to-local limit. We also state some open questions and describe recent related progress.

Citations

• Numerical viscosity and the entropy condition for conservative difference schemes

Cited by

• Asymptotically compatible entropy-consistent discretization for a class of nonlocal conservation laws

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