arXiv subjects
Publications and source records attributed to M. Ruzicka.
In this work we treat the space-time discretization of the generalized Stokes equations in the case of Dirichlet boundary conditions. We prove error estimates in the case $p\in[\frac{2d}{d+2},\infty)$ that are independent of the degeneracy parameter $\delta\in[0,\delta_0]$. For $p\leq 2$, our convergence rate is optimal.
In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.
In this paper we study the existence of weak solutions to an unsteady system describing the motion of micro-polar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. Using the Lipschitz truncation and the solenoidal Lipschitz truncation we establish the existence of global solutions for shear exponents $p>6/5$ in three-dimensional domains.