Global regularity for a 1D Euler-alignment system with misalignment

Abstract

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly singular short-range alignment interaction, the solution is globally regular, despite the effect of misalignment.

38 pages, 1 figure

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment

Cited by in corpus (1)

• Eulerian dynamics in multi-dimensions with radial symmetry