5 papers · 1 filter
Geometric Structure of Mass Concentration Sets for Pressureless Euler Alignment Systems
Daniel Lear, Trevor M. Leslie, Roman Shvydkoy +1
We study the limiting dynamics of the Euler Alignment system with a smooth, heavy-tailed interaction kernel and unidirectional velocity . We dem…
On the Lagrangian Trajectories for the One-Dimensional Euler Alignment Model without Vacuum Velocity
Trevor M. Leslie
A well-known result of Carrillo, Choi, Tadmor, and Tan states that the 1D Euler Alignment model with smooth interaction kernels possesses a 'critical threshold' criterion for the g…
On the Structure of Limiting Flocks in Hydrodynamic Euler Alignment Models
Trevor M. Leslie, Roman Shvydkoy
The goal of this note is to study limiting behavior of a self-organized continuous flock evolving according to the 1D hydrodynamic Euler Alignment model. We provide a series of qua…
Weak and Strong Solutions to the Forced Fractional Euler Alignment System
Trevor M. Leslie
We consider a hydrodynamic model of self-organized evolution of agents, with singular interaction kernel (), in the presence of an additional external f…
The Energy Balance Relation for Weak solutions of the Density-Dependent Navier-Stokes Equations
Trevor Leslie, Roman Shvydkoy
We consider the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the e…