Modeling of flows through a channel by the Navier–Stokes variational inequalities

0540784 - MÚ 2022 RIV CZ eng J - Journal Article
Kračmar, S. - Neustupa, Jiří
Modeling of flows through a channel by the Navier–Stokes variational inequalities.
Acta Polytechnica. Roč. 61, SI (2021), s. 89-98. ISSN 1210-2709. E-ISSN 1805-2363
Institutional support: RVO:67985840
Keywords : Navier-Stokes equation * variational inequality * do nothing outflow boundary condition
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.14311/AP.2021.61.0089

We deal with a mathematical model of a flow of an incompressible Newtonian fluid through a channel with an artificial boundary condition on the outflow. We explain how several artificial boundary conditions formally follow from appropriate variational formulations and the way one expresses the dynamic stress tensor. Predominantly considered to be the most appropriate from the physical point of view, does not enable one to derive an energy inequality, we explain how this problem can be overcome by using variational inequalities. We derive a priori estimates, which are the core of the proofs, and present theorems on the existence of solutions in the unsteady and steady cases.
Permanent Link: http://hdl.handle.net/11104/0318382