Stability of critical shapes for the drag minimization problem in Stokes flow

DOI10.1016/j.matpur.2013.01.003zbMath1278.49048OpenAlexW2033062896MaRDI QIDQ391376

Fabien Caubet, Marc Dambrine

Publication date: 10 January 2014

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2013.01.003

zbMATH Keywords

Stokes equationsdrag minimizationoptimal profilesshape calculusshape Hessianstability of critical shape

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimization of shapes other than minimal surfaces (49Q10) Flow control and optimization for incompressible viscous fluids (76D55) PDEs in connection with control and optimization (35Q93)

Related Items (5)

Computing quantities of interest for random domains with second order shape sensitivity analysis ⋮ On the Detection of Small Moving Disks in a Fluid ⋮ Stability in shape optimization with second variation ⋮ Steady Navier-Stokes equations in planar domains with obstacle and explicit bounds for unique solvability ⋮ Eight(y) mathematical questions on fluids and structures

Cites Work

• Minimality via second variation for a nonlocal isoperimetric problem
• Equilibrium configurations of epitaxially strained elastic films: second-order minimality conditions and qualitative properties of solutions
• A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid
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• Instability of an Inverse Problem for the Stationary Navier--Stokes Equations
• DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS
• On Second Order Shape Optimization Methods for Electrical Impedance Tomography
• Differentiation with Respect to the Domain in Boundary Value Problems
• The Differentiability of the Drag with Respect to the Variations of a Lipschitz Domain in a Navier--Stokes Flow
• About stability of equilibrium shapes
• Prolongement Unique Des Solutions
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