Long-time behavior of shape design solutions for the Navier-Stokes equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00569947" target="_blank" >RIV/67985840:_____/23:00569947 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/zamm.202100441" target="_blank" >https://doi.org/10.1002/zamm.202100441</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/zamm.202100441" target="_blank" >10.1002/zamm.202100441</a>

Result language
angličtina
Original language name
Long-time behavior of shape design solutions for the Navier-Stokes equations
Original language description
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the (Formula presented.) -topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property. As a consequence, we show that the asymptotic convergence of shape solutions for parabolic/elliptic problems is a particular case of our analysis. Last, a numerical example is provided to show the occurrence of the convergence of shape design solutions of time-dependent problems with different values of the terminal time T to a shape design solution of the stationary problem.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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