Abstract
We assume that \(\Omega ^{t}\) (for t ∈ [0, T]) is a time-varying domain in \(\mathbb{R}^{3}\). Particularly, \(\Omega ^{t}\) can be a region around colliding bodies. Under certain conditions on \(\Omega ^{t}\) and the way it varies, we prove the weak solvability of the Navier–Stokes system with Navier’s slip boundary condition in \(Q_{(0,T)}:=\{ (\mathbf{x},t);\ 0 < t < T,\ \mathbf{x} \in \Omega ^{t}\}\).
Dedicated to Professor Yoshihiro Shibata on the occasion of his 60th birthday.
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Acknowledgements
The research has been supported by the Grant Agency of the Czech Republic (grant No. 13-00522S), by the Academy of Sciences of the Czech Republic (RVO 67985840) and by the University of Sud Toulon-Var.
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Neustupa, J., Penel, P. (2016). A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_20
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