2 citations · 8 across the 15 of their papers we have counts for
5 papers · 1 filter
Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors
Claudiu Mîndrilă, Sebastian Schwarzacher
We provide existence of very weak solutions and new a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. To…
A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
Olli Saari, Sebastian Schwarzacher
We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty…
Two-speed solutions to non-convex rate-independent systems
Filip Rindler, Sebastian Schwarzacher, Juan J. L. Velazquez
We consider evolutionary PDE inclusions of the form \[ -λ\dot{u}_λ+ Δu - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in ,} \] where $\math…
Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions
Boris Muha, Sebastian Schwarzacher
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-…
Global higher integrability of weak solutions of porous medium systems
Kristian Moring, Christoph Scheven, Sebastian Schwarzacher +1
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{equation*} \partial_t u-Δ(|u|^…