scholarly journals Asymptotic Behavior of the Navier--Stokes System in a Thin Domain with Navier Condition on a Slightly Rough Boundary

2013 ◽  
Vol 45 (3) ◽  
pp. 1641-1674 ◽  
Author(s):  
J. Casado-Díaz ◽  
M. Luna-Laynez ◽  
F. J. Suárez-Grau
Keyword(s):  
Asymptotic Behavior ◽  
Stokes System ◽  
Navier Stokes ◽  
Rough Boundary ◽  
Thin Domain ◽  
Navier Condition

scholarly journals Self-propelled motion of a rigid body inside a density dependent incompressible fluid

2020 ◽  
Author(s):  
Sarka Necasova ◽  
Mythily Ramaswamy ◽  
Arnab Roy ◽  
Anja Schlomerkemper
Keyword(s):  
Angular Momentum ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Rigid Body ◽  
Incompressible Fluid ◽  
Stokes System ◽  
Navier Stokes ◽  
Navier Condition ◽  
Whole Space

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole space. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the  balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.

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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