Article Contents
Article Contents

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

• 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 $\mathbf{V}$ and described by the family of domains $\Omega_t$ parametrized by $t\in[0,T]$. 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 $r\ge11/5$.
Mathematics Subject Classification: Primary: 35Q30, 76D55; Secondary: 35R37.

 Citation:

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