Geodesic
The topological asymptotic for the Navier-Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 401-425

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The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional and a numerical application is presented.

DOI : 10.1051/cocv:2005012
Classification : 35J60, 49Q10, 49Q12, 76D05, 76D55
Keywords: shape optimization, topological asymptotic, Navier-Stokes equations 
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     author = {Amstutz, Samuel},
     title = {The topological asymptotic for the {Navier-Stokes} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {401--425},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {3},
     year = {2005},
     doi = {10.1051/cocv:2005012},
     mrnumber = {2148851},
     zbl = {1123.35040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005012/}
}
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Amstutz, Samuel. The topological asymptotic for the Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 401-425. doi: 10.1051/cocv:2005012

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