This paper studies the global existence and uniqueness of strong solutions and its large-Time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic Cucker-Smale flocking equation with strong local alignment forces and diffusions through the hydrodynamic limit based on the relative entropy argument. In a perturbation framework, we establish the global existence of a unique strong solution for the system under suitable smallness and regularity assumptions on the initial data. We also provide the large-Time behavior of solutions showing the fluid density and the velocity converge to its averages exponentially fast as time goes to infinity.
|Number of pages||23|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2019 Jan 1|
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics