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

0569947 - MÚ 2024 RIV DE eng J - Journal Article
Simon, John Sebastian
Long-time behavior of shape design solutions for the Navier-Stokes equations.
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. Roč. 103, č. 2 (2023), č. článku e202100441. ISSN 0044-2267. E-ISSN 1521-4001
Institutional support: RVO:67985840
Keywords : flow of fluids * shape optimization
OECD category: Pure mathematics
Impact factor: 2.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/zamm.202100441

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.
Permanent Link: https://hdl.handle.net/11104/0341263