Abstract:
Euler alignment system is a hydrodynamic limit for kinetic flocking models. With a singular influence function, it is also closely related to fractional Burgers equation. It is well-known that in the supercritical case, solutions for fractional Burgers equation can lead to finite time blowup, as dissipation is too weak to overcome convection. However, we prove a surprising result: with a density dependent dissipation, the solution for fractional Euler alignment system is globally regular, as density enhances dissipation. This is a joint work with T. Do, A. Kiselev and L. Ryzhik. |