scholarly journals On Uniqueness for the Navier–Stokes System in 3D-Bounded Lipschitz Domains

2002 ◽  
Vol 195 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Sylvie Monniaux
Keyword(s):  
Stokes System ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Bounded Lipschitz Domains

scholarly journals Lq-Estimates for stationary Stokes system with coefficients measurable in one direction

2019 ◽  
Vol 09 (01) ◽  
pp. 1950004 ◽  
Author(s):  
Hongjie Dong ◽  
Doyoon Kim
Keyword(s):  
Stokes System ◽  
A Priori ◽  
Lipschitz Constant ◽  
Variable Coefficients ◽  
Lipschitz Domains ◽  
Small Ball ◽  
Fixed Direction ◽  
Measurable Functions ◽  
Whole Space ◽  
Bounded Lipschitz Domains

We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori [Formula: see text]-estimates for any [Formula: see text] when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a [Formula: see text]-estimate and prove the solvability for any [Formula: see text] when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.

scholarly journals Besov regularity for the stationary Navier–Stokes equation on bounded Lipschitz domains

2017 ◽  
Vol 97 (3) ◽  
pp. 466-485 ◽  
Author(s):  
Frank Eckhardt ◽  
Petru A. Cioica-Licht ◽  
Stephan Dahlke
Keyword(s):  
Stokes Equation ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Navier Stokes Equation ◽  
Besov Regularity ◽  
Bounded Lipschitz Domains

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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