Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients

2020 ◽  
Vol 194 ◽  
pp. 111355
Author(s):  
Shuang Liang ◽  
Shenzhou Zheng
Keyword(s):  
Stokes System ◽  
Bmo Coefficients

scholarly journals Wolff type potential estimates for stationary Stokes systems with Dini-BMO coefficients

2020 ◽  
pp. 2050064
Author(s):  
Lingwei Ma ◽  
Zhenqiu Zhang
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Stokes System ◽  
Gradient Estimate ◽  
Regularity Assumption ◽  
Stokes Systems ◽  
Pointwise Bound ◽  
Nonlinear Potential ◽  
Bmo Coefficients ◽  
Type Potential

The pointwise gradient estimate for weak solution pairs to the stationary Stokes system with Dini-[Formula: see text] coefficients is established via the Havin–Maz’ya–Wolff type nonlinear potential of the nonhomogeneous term. In addition, we present a pointwise bound for the weak solutions under no extra regularity assumption on the coefficients.

Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains

2019 ◽  
Vol 17 (04) ◽  
pp. 569-596
Author(s):  
Lingwei Ma ◽  
Zhenqiu Zhang ◽  
Qi Xiong
Keyword(s):  
Weak Solution ◽  
Maximal Function ◽  
Stokes System ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Stokes Systems ◽  
Solution Pair ◽  
Reifenberg Flat Domains ◽  
Bmo Coefficients ◽  
Reifenberg Flat

Pointwise estimates of weak solution pairs to a stationary Stokes system with small [Formula: see text] semi-norm coefficients are established in Reifenberg flat domains by using the restricted sharp maximal function. These pointwise estimates provide a unified treatment of the Calderón–Zygmund estimates for the solution pair to Stokes systems in [Formula: see text] and [Formula: see text] spaces.

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

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.

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