Regular Solutions to the Coagulation Equations with Singular Kernels

2012/10/04 by Carlos Cueto Camejo, Camejo, Carlos Cueto, Robin Gröpler +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1210.1500

openalex publication_date 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove the existence of solutions to the coagulation equation with singular kernels. We use weighted L¹-spaces to deal with the singularities in order to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak L¹ compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also mentioned.

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