Formation of singularities for multi-dimensional transport equations with nonlocal velocity

2021/11/02 by Quansen Jiu, Jiu, Quansen, Wanwan Zhang +1 · 1 citation
Engineering · Mathematics · #35B35 #35Q35 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.01444

openalex publication_date 2021/11/02 · openalex created_date 2022/10/09 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a class of multi-dimensional transport equations with nonlocal velocity. It is shown that the local smooth solution cannot exist globally in time via the De Giorgi iteration technique.

Cited by

• Finite time blow-up for a multi-dimensional model of the Kiselev-Sarsam equation

Related

• On the local and global existence of solutions to 1D transport equations with nonlocal velocity
• On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation
• Global existence for some transport equations with nonlocal velocity
• A Note on Singularity Formation for a Nonlocal Transport Equation
• On the blowup of solutions for a nonlocal multi-dimensional transport equation