Shape optimization for non-Newtonian fluids in time-dependent domains

0430330 - MÚ 2015 RIV US eng J - Journal Article
Sokolowski, J. - Stebel, Jan
Shape optimization for non-Newtonian fluids in time-dependent domains.
Evolution Equations and Control Theory. Roč. 3, č. 2 (2014), s. 331-348. ISSN 2163-2480. E-ISSN 2163-2480
R&D Projects: GA ČR GA201/09/0917
Institutional support: RVO:67985840
Keywords : shape optimization * time-dependent domain * incompressible viscous fluid
Subject RIV: BA - General Mathematics
Impact factor: 0.373, year: 2014
http://www.aimsciences.org/journals/home.jsp?journalID=25

We study the model of an incompressible non-Newtonian fluid in a moving domain. The domain is defined as a tube built by the velocity field V and described by the family of domains $Omega_t$ parametrized by $tin[0,T]$. A new shape optimization problem associated with the model is defined for a family of initial domains $Omega_0$ and admissible velocity vector fields. It is shown that such shape optimization problems are well posed under the classical conditions on compactness of the admissible shapes [18]. For the state problem, we prove the existence of weak solutions and their continuity with respect to perturbations of the time-dependent boundary, provided that the power-law index $rge11/5$.
Permanent Link: http://hdl.handle.net/11104/0235285