The global Cauchy problem for compressible Euler equations with a nonlocal dissipation

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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.

Original languageEnglish
Pages (from-to)185-207
Number of pages23
JournalMathematical Models and Methods in Applied Sciences
Issue number1
Publication statusPublished - 2019 Jan 1


All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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