Compactness for nonlinear transport equations

2011/08/19 by Fethi Ben Belgacem, Pierre-Emmanuel Jabin, Pierre‐Emmanuel Jabin +2
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1108.4020

arxiv created 2011/08/19 · openalex publication_date 2011/08/19 · arxiv updated 2011/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which gives quantitative compactness estimates compatible with both frameworks.

Citations

• On commutators of singular integrals and bilinear singular integrals

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