Global well-posedness, regularity and blow-up for the β-CCF model

Abstract

The paper is concerned with the β-CCF model which is a 1D nonlocal nonlinear transport model. The velocity is coupled via a composition of the Hilbert transform and Riesz potentials, giving rise to three basic cases that reflect the balance between the nonlinearity and dissipation, namely the subcritical, critical and supercritical ranges. In our analysis we consider those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and blow-up of solutions.