Existence of global weak solutions for Navier-Stokes-Poisson equations with quantum effect and convergence to incompressible Navier-Stokes equations

2014 ◽  
Vol 38 (17) ◽  
pp. 3629-3641 ◽  
Author(s):  
Jianwei Yang ◽  
Qiangchang Ju
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Quantum Effect ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equations ◽  
Poisson Equations

scholarly journals Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations

2013 ◽  
Vol 45 (6) ◽  
pp. 3431-3452 ◽  
Author(s):  
Andrea R. Nahmod ◽  
Nataša Pavlović ◽  
Gigliola Staffilani
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equations

STUDY OF A GENERALIZED FRAGMENTATION MODEL FOR SPRAYS

2009 ◽  
Vol 06 (01) ◽  
pp. 185-206 ◽  
Author(s):  
NICHOLAS LEGER ◽  
ALEXIS F. VASSEUR
Keyword(s):  
Mathematical Model ◽  
Kinetic Equation ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fragmentation Model ◽  
Global Weak Solutions ◽  
Navier Stokes Equations ◽  
Drag Forces ◽  
Break Up

We study a mathematical model for sprays which takes into account particle break-up due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier–Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system.

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