The global classical solution to compressible Euler system with velocity alignment

Abstract

In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric hyperbolic type. The global existence and uniqueness of smooth solution for small initial data is provided.

Keywords

• non-local velocity alignment
• global existence
• nonlinear pressure