We present a variational approach for the construction of Leray-Hopf solutions to the non-newtonian Navier-Stokes system. Inspired by the work OSS18 on the corresponding Newtonian problem, we minimise certain stabilised Weighted Inertia-Dissipation-Energy (WIDE) functionals and pass to the limit of a vanishing parameter in order to recover a Leray-Hopf solution of the non-newtonian Navier-Stokes equations. It turns out that the results differ depending on the rheology of the fluid. The investigation of the non-newtonian Navier-Stokes system via this variational approach is motivated by the fact that it is particularly well suited to gain insights into weak, respectively strong convergence properties for different flow-behaviour exponents and thus into possibly turbulent behaviour of the fluid flow. ...
%0 Generic
%1 lienstromberg2023variational
%A Lienstromberg, Christina
%A Schiffer, Stefan
%A Schubert, Richard
%D 2023
%K Lienstromberg Schubert IADM Schiffer Navier-Stokes ProjektPN3-13 PN3-13
%R doi:10.48550/ARXIV.2312.03546
%T A variational approach to the non-newtonian Navier-Stokes equations
%U https://arxiv.org/abs/2312.03546
%X We present a variational approach for the construction of Leray-Hopf solutions to the non-newtonian Navier-Stokes system. Inspired by the work OSS18 on the corresponding Newtonian problem, we minimise certain stabilised Weighted Inertia-Dissipation-Energy (WIDE) functionals and pass to the limit of a vanishing parameter in order to recover a Leray-Hopf solution of the non-newtonian Navier-Stokes equations. It turns out that the results differ depending on the rheology of the fluid. The investigation of the non-newtonian Navier-Stokes system via this variational approach is motivated by the fact that it is particularly well suited to gain insights into weak, respectively strong convergence properties for different flow-behaviour exponents and thus into possibly turbulent behaviour of the fluid flow. ...
@preprint{lienstromberg2023variational,
abstract = {We present a variational approach for the construction of Leray-Hopf solutions to the non-newtonian Navier-Stokes system. Inspired by the work [OSS18] on the corresponding Newtonian problem, we minimise certain stabilised Weighted Inertia-Dissipation-Energy (WIDE) functionals and pass to the limit of a vanishing parameter in order to recover a Leray-Hopf solution of the non-newtonian Navier-Stokes equations. It turns out that the results differ depending on the rheology of the fluid. The investigation of the non-newtonian Navier-Stokes system via this variational approach is motivated by the fact that it is particularly well suited to gain insights into weak, respectively strong convergence properties for different flow-behaviour exponents and thus into possibly turbulent behaviour of the fluid flow. ...},
added-at = {2024-01-12T15:03:11.000+0100},
archiveprefix = {arXiv},
author = {Lienstromberg, Christina and Schiffer, Stefan and Schubert, Richard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2fcf9e55c78149cf5016d37ee60cbd25a/mathematik},
doi = {doi:10.48550/ARXIV.2312.03546},
eprint = {2312.03546},
interhash = {52f586b8ce72a3ef98b5d2a716beef6a},
intrahash = {fcf9e55c78149cf5016d37ee60cbd25a},
keywords = {Lienstromberg Schubert IADM Schiffer Navier-Stokes ProjektPN3-13 PN3-13},
primaryclass = {math.AP},
timestamp = {2024-05-29T16:06:28.000+0200},
title = {A variational approach to the non-newtonian Navier-Stokes equations},
url = {https://arxiv.org/abs/2312.03546},
year = 2023
}
