%0 Generic %1 lienstromberg2023variational %A Lienstromberg, Christina %A Schiffer, Stefan %A Schubert, Richard %D 2023 %K 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 = {2024-01-12T15:03:12.000+0100}, archiveprefix = {arXiv}, author = {Lienstromberg, Christina and Schiffer, Stefan and Schubert, Richard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2fcf9e55c78149cf5016d37ee60cbd25a/simtech}, doi = {doi:10.48550/ARXIV.2312.03546}, eprint = {2312.03546}, interhash = {52f586b8ce72a3ef98b5d2a716beef6a}, intrahash = {fcf9e55c78149cf5016d37ee60cbd25a}, keywords = {PN3-13}, primaryclass = {math.AP}, timestamp = {2024-01-12T15:04:17.000+0100}, title = {A variational approach to the non-newtonian Navier-Stokes equations}, url = {https://arxiv.org/abs/2312.03546}, year = 2023 }