Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel
Debora Amadori, Cleopatra C. Christoforou · Nonlinear Analysis · 2024
We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in Amadori and Christoforou (2022) 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, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.