scholarly journals Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations

2011 ◽  
Vol 65 (4) ◽  
pp. 549-585 ◽  
Author(s):  
Xiangdi Huang ◽  
Jing Li ◽  
Zhouping Xin
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Well Posedness ◽  
Navier Stokes Equations

scholarly journals On well-posedness of a magnetization-variables model for Navier-Stokes equations with damping

2020 ◽  
Author(s):  
Abdelkerim Chaabani,
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Well Posedness ◽  
Energy Methods ◽  
Damping Term ◽  
Navier Stokes Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

This paper aims to establish existence and uniqueness results of weak and strong solution to the three-dimensional periodic magnetization-variables formulation to Navier-Stokes equations with damping term. Authors in precedent works addressed the question as to whether this model and similar ones without damping term possess a weak solution. In this vein, considering a damping term in the magnetization-variable formulation turned to be consequential as it enforces existence and uniqueness results. Energy methods, compactness methods are the main tools.

GLOBAL CLASSICAL SOLUTIONS FOR A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

2013 ◽  
Vol 10 (03) ◽  
pp. 537-562 ◽  
Author(s):  
MYEONGJU CHAE ◽  
KYUNGKEUN KANG ◽  
JIHOON LEE
Keyword(s):  
Stokes Equations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
Interaction Model ◽  
Planck Equation ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Navier Stokes Equations ◽  
Global Classical Solutions ◽  
System Coupling

We consider a system coupling the compressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation on three-dimensional torus. The coupling arises from a drag force exerted by each other. We establish the existence of the global classical solutions close to an equilibrium, and further prove that the solutions converge to the equilibrium exponentially fast.

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