scholarly journals Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions

2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Václav Mácha ◽  
Jakub Tichý
Keyword(s):  
Boundary Conditions ◽  
Hölder Continuity ◽  
Shear Thinning ◽  
Slip Boundary Conditions ◽  
Holder Continuity ◽  
Slip Boundary ◽  
Shear Thinning Fluids ◽  
Velocity Gradients ◽  
Perfect Slip Boundary Conditions

Boundary regularity of flows under perfect slip boundary conditions

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Petr Kaplický ◽  
Jakub Tichý
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Boundary Regularity ◽  
Growth Conditions ◽  
Regularity Of Solutions ◽  
Slip Boundary Conditions ◽  
Optimal Regularity ◽  
Slip Boundary ◽  
Nonlinear Elliptic ◽  
Perfect Slip Boundary Conditions

AbstractWe investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

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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