Filters

20212

More filters

20222
Reset filters

Settings

Author: Hopf, Katharina × Author: Mielke, Alexander × End date: 2022 × Start date: 2020 ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Eiter, Thomas; Hopf, Katharina; Mielke, Alexander
    We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba--Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.
  • Thumbnail Image
    Item
    Global existence analysis of energy-reaction-diffusion systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander
    We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.