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On a vorticity minimization problem for the stationary 2D Stokes equations
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Abstract
This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.
참고문헌 (9)
- "\it On some control problems in fluid mechanics}", pp.303~ (1990)
- "it On traces for $H $ in Lipschitz domains}", pp.845~ (2002), Buffa} A. Buffa
- "\it Lectures on optimization--theory and algorithms} Tata Institute of Fundamental Research Lectures on Mathematics and Physics Tata Institute of Fundamental Research" (1978)
- "\it Introduction to numerical linear algebra and optimization}" (1991), Cambridge University Press
- "\it Mathematical analysis and numerical methods for science andtechnology}", 6. etion problems. ii (1993), Springer-Verlag
- "\it On Some Finite Element Methods for the Numerical Simulationof Incompressible Viscous Flow}", pp.17~ (1993), IncompressibleComputational Fluid Dynamics Trends and Advances Cambridge University Press
- "\it Finite element methods for Navier-Stokes equations}", girault and p. raart (1986), Theoryand algorithms. Springer-Verlag
- "\it The mathematical theory of viscous incompressible flow}" (1963), Gordon and Breach Science Publishers
- "\it Hilbert space methods for partial differential equations} Electronic reprint of the 1977 original Electronic Monographs in Differential Equations" (1994)
관련 논문AI추천
Existence of quasi-stationary Stokes flow in a dihedral domain진범자대한수학회 · 대한수학회지2006 · 제43권 제4호A boundary control problem for vorticity minimization in time-dependent 2D Navier-Stokes equations김홍철강원경기수학회 · 한국수학논문집2015 · 제23권 제2호On the improved regularity criterion of the solutions to the Navier-Stokes equationsSadek Gala대한수학회 · 대한수학회논문집2020 · 제35권 제1호Regularity of weak solutions of the compressible Navier-Stokes equations진범자, 최희준대한수학회 · 대한수학회지2003 · 제40권 제6호Temporal and spatial decay rates of Navier-Stokes solutions in exterior domains배형옥, 진범자대한수학회 · 대한수학회보2007 · 제44권 제3호Analyticity for the Stokes Operator in Besov spaces배형옥대한수학회 · 대한수학회지2003 · 제40권 제6호
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