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

Author(s):  
Przemysław Kosewski ◽  
Kamil Wołos

2019 ◽  
Vol 25 (1) ◽  
pp. 111-117 ◽  
Author(s):  
T. Tachim Medjo

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.



2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  


2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad

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.



2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Jankuhn ◽  
Maxim A. Olshanskii ◽  
Arnold Reusken ◽  
Alexander Zhiliakov

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.



2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi

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.



2013 ◽  
Vol 51 (6) ◽  
pp. 3327-3350 ◽  
Author(s):  
Hyea Hyun Kim ◽  
Eric T. Chung ◽  
Chak Shing Lee


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