scholarly journals Existence and regularity result for Stokes system with special inlet/outlet condition

2021 ◽  
Author(s):  
Przemysław Kosewski ◽  
Kamil Wołos
Keyword(s):  
Stokes System ◽  
Regularity Result

A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system

2019 ◽  
Vol 25 (1) ◽  
pp. 111-117 ◽  
Author(s):  
T. Tachim Medjo
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Stokes Equations ◽  
Regularity Result ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Weak Formulation ◽  
Navier Stokes Equations ◽  
Regularity Of Weak Solutions ◽  
Dimensional Domain

Abstract In this article, we study a coupled Allen–Cahn–Navier–Stokes model in a two-dimensional domain. The model consists of the Navier–Stokes equations for the velocity, coupled with an Allen–Cahn model for the order (phase) parameter. We present an equivalent weak formulation for the model, and we prove a new regularity result for the weak solutions.

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 On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

Error analysis of higher order trace finite element methods for the surface Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Jankuhn ◽  
Maxim A. Olshanskii ◽  
Arnold Reusken ◽  
Alexander Zhiliakov
Keyword(s):  
Finite Element ◽  
Stokes System ◽  
Parametric Representation ◽  
Higher Order ◽  
Optimal Order ◽  
Helmholtz Instability ◽  
Surface Stability ◽  
Instability Problem ◽  
Convergence Results ◽  
Optimal Order Convergence

AbstractThe paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.

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.

A Staggered Discontinuous Galerkin Method for the Stokes System

2013 ◽  
Vol 51 (6) ◽  
pp. 3327-3350 ◽  
Author(s):  
Hyea Hyun Kim ◽  
Eric T. Chung ◽  
Chak Shing Lee
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Stokes System ◽  
Staggered Discontinuous Galerkin Method
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