scholarly journals Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains

2019 ◽  
Vol 150 (5) ◽  
pp. 2255-2300 ◽  
Author(s):  
Ondřej Kreml ◽  
Šárka Nečasová ◽  
Tomasz Piasecki
Keyword(s):  
Boundary Conditions ◽  
Stokes System ◽  
Local Existence ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Strong Uniqueness ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Moving Domains ◽  
Open Question

AbstractWe consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.

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.

scholarly journals On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

2010 ◽  
Vol 13 (4) ◽  
pp. 783-798 ◽  
Author(s):  
Donatella Donatelli ◽  
◽  
Eduard Feireisl ◽  
Antonín Novotný ◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Stokes System ◽  
Unbounded Domains ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Slip Boundary

scholarly journals Weak solutions to the barotropic Navier–Stokes system with slip boundary conditions in time dependent domains

2013 ◽  
Vol 254 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Eduard Feireisl ◽  
Ondřej Kreml ◽  
Šárka Nečasová ◽  
Jiří Neustupa ◽  
Jan Stebel
Keyword(s):  
Boundary Conditions ◽  
Weak Solutions ◽  
Stokes System ◽  
Time Dependent ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Slip Boundary

NAVIER–STOKES SYSTEM ON THE FLAT CYLINDER AND UNIT SQUARE WITH SLIP BOUNDARY CONDITIONS

2010 ◽  
Vol 12 (02) ◽  
pp. 325-349 ◽  
Author(s):  
EFIM DINABURG ◽  
DONG LI ◽  
YAKOV G. SINAI
Keyword(s):  
Boundary Conditions ◽  
Initial Velocity ◽  
Stokes System ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Unit Square ◽  
Slip Boundary

We study the decay of Fourier modes of solutions to the two-dimensional Navier–Stokes System on a flat cylinder and the unit square with slip boundary conditions. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes.

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