scholarly journals Vanishing viscosity limit of the 3D incompressible micropolar equations in a bounded domain

Author(s):  
Yangyang Chu ◽  
Yuelong Xiao

In this paper, we study the vanishing viscosity limit for the 3D incompressible micropolar equations in a flat domain with boundary conditions. We prove the existence of the global weak solution of the micropolar equations and obtain the uniform estimate of the strong solution. Furthermore, we establish the convergence rate from the solution of the micropolar equations to that of the ideal micropolar equations as all viscosities tend to zero (i.e., (ε,χ,γ,κ) → 0).

Author(s):  
Danica Basarić

AbstractWe identify a class of measure-valued solutions of the barotropic Euler system on a general (unbounded) spatial domain as a vanishing viscosity limit for the compressible Navier–Stokes system. Then we establish the weak (measure-valued)–strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.


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