scholarly journals Existence of global weak solutions of $ p $-Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jian-Guo Liu ◽  
Zhaoyun Zhang
2013 ◽  
Vol 45 (6) ◽  
pp. 3431-3452 ◽  
Author(s):  
Andrea R. Nahmod ◽  
Nataša Pavlović ◽  
Gigliola Staffilani

2009 ◽  
Vol 06 (01) ◽  
pp. 185-206 ◽  
Author(s):  
NICHOLAS LEGER ◽  
ALEXIS F. VASSEUR

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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