BV solutions for a hydrodynamic model of flocking--type with all-to-all interaction kernel

Abstract

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish global existence of entropy weak solutions with concentration to the Cauchy problem for any BV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein. In addition, under a suitable condition on the initial data, we show that entropy weak solutions with concentration admit time-asymptotic flocking.

59 pages, 1 figure

References in corpus (1)

• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment

Cited by in corpus (2)

• The sticky particle dynamics of the 1D pressureless Euler-alignment system as a gradient flow
• Sticky particle Cucker-Smale dynamics and the entropic selection principle for the 1D Euler-alignment system