A pointwise regularity criterion for axisymmetric Navier–Stokes system

2018 ◽  
Vol 461 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Zujin Zhang
Keyword(s):  
Stokes System ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Pointwise Regularity

scholarly journals A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain

2019 ◽  
Vol 64 (4) ◽  
pp. 397-407
Author(s):  
Jishan Fan ◽  
Xuanji Jia ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Stokes System ◽  
Regularity Criterion ◽  
Navier Stokes

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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