scholarly journals Singularities of certain finite energy solutions to the Navier-Stokes system

2020 ◽  
Vol 40 (1) ◽  
pp. 189-206 ◽  
Author(s):  
Grzegorz Karch ◽  
◽  
Maria E. Schonbek ◽  
Tomas P. Schonbek ◽  
◽  
...  
Keyword(s):  
Stokes System ◽  
Finite Energy ◽  
Navier Stokes

scholarly journals Semiflow selection for the compressible Navier–Stokes system

2020 ◽  
Author(s):  
Danica Basarić
Keyword(s):  
Initial Data ◽  
Open Problem ◽  
Stokes System ◽  
Initial Density ◽  
Finite Energy ◽  
Navier Stokes ◽  
State Variables ◽  
Semigroup Property ◽  
Almost Everywhere ◽  
Selection For

Abstract Although the existence of dissipative weak solutions for the compressible Navier–Stokes system has already been established for any finite energy initial data, uniqueness is still an open problem. The idea is then to select a solution satisfying the semigroup property, an important feature of systems with uniqueness. More precisely, we are going to prove the existence of a semiflow selection in terms of the three state variables: the density, the momentum, and the energy. Finally, we will show that it is possible to introduce a new selection defined only in terms of the initial density and momentum; however, the price to pay is that the semigroup property will hold almost everywhere in time.

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.

Homogenization of the time discretized compressible Navier–Stokes system

2012 ◽  
Vol 75 (4) ◽  
pp. 2486-2498 ◽  
Author(s):  
Hongxing Zhao ◽  
Zheng-an Yao
Keyword(s):  
Stokes System ◽  
Navier Stokes
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