scholarly journals Strong Solutions to the Compressible Navier--Stokes--Vlasov--Fokker--Planck Equations: Global Existence Near the Equilibrium and Large Time Behavior

2017 ◽  
Vol 49 (2) ◽  
pp. 984-1026 ◽  
Author(s):  
Fucai Li ◽  
Yanmin Mu ◽  
Dehua Wang
Keyword(s):  
Global Existence ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Time Behavior ◽  
Fokker Planck Equations ◽  
Fokker Planck

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

2019 ◽  
Vol 29 (01) ◽  
pp. 185-207 ◽  
Author(s):  
Young-Pil Choi
Keyword(s):  
Global Existence ◽  
Euler Equations ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Local Alignment ◽  
Time Behavior ◽  
Unique Strong Solution ◽  
Global Existence And Uniqueness ◽  
Isothermal Euler Equations

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.

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