scholarly journals Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions

2016 ◽  
Vol 54 (1) ◽  
pp. 221-250 ◽  
Author(s):  
Sergio Frigeri ◽  
Elisabetta Rocca ◽  
Jürgen Sprekels
Keyword(s):  
Distributed Control ◽  
Stokes System ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Optimal Distributed Control

Optimal distributed-control of vortices in Navier–Stokes flows

2005 ◽  
Vol 341 (3) ◽  
pp. 147-152
Author(s):  
Slim Chaabane ◽  
Jamel Ferchichi ◽  
Karl Kunisch
Keyword(s):  
Distributed Control ◽  
Navier Stokes ◽  
Stokes Flows ◽  
Optimal Distributed Control

scholarly journals Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bo You
Keyword(s):  
Stokes System ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Time Behavior ◽  
Contact Lines ◽  
Trajectory Attractor ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Long Time ◽  
Statistical Solutions

<p style='text-indent:20px;'>The objective of this paper is to consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. As we know, it is very difficult to obtain the uniqueness of an energy solution for this system even in two dimensions caused by the presence of the strong coupling at the boundary. Thus, we first prove the existence of a trajectory attractor for such system, which is a minimal compact trajectory attracting set for the natural translation semigroup defined on the trajectory space. Furthermore, based on the abstract results (trajectory attractor approach) developed in [<xref ref-type="bibr" rid="b38">38</xref>], we construct trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines.</p>

scholarly journals On the stationary nonlocal Cahn–Hilliard–Navier–Stokes system: Existence, uniqueness and exponential stability

2020 ◽  
pp. 1-41
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan ◽  
Lakshmi Naga Mahendranath Perisetti
Keyword(s):  
Weak Solution ◽  
Stokes System ◽  
Two Dimensions ◽  
Immiscible Fluids ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Browder’S Theorem ◽  
Exponentially Stable ◽  
Mobility Parameter ◽  
Regularity Results

The Cahn–Hilliard–Navier–Stokes system describes the evolution of two isothermal, incompressible, immiscible fluids in a bounded domain. In this work, we consider the stationary nonlocal Cahn–Hilliard–Navier–Stokes system in two and three dimensions with singular potential. We prove the existence of a weak solution for the system using pseudo-monotonicity arguments and Browder’s theorem. Further, we establish the uniqueness and regularity results for the weak solution of the stationary nonlocal Cahn–Hilliard–Navier–Stokes system for constant mobility parameter and viscosity. Finally, in two dimensions, we establish that the stationary solution is exponentially stable (for convex singular potentials) under suitable conditions on mobility parameter and viscosity.

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
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