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search.filters.applied.f.access: openAccess × Author: Mielke, Alexander × Start date: 2017 × DDC: 510 × Has files: Yes × Subject: energy estimates ×

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    Thermoviscoelasticity in Kelvin--Voigt rheology at large strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Mielke, Alexander; Roubíček, Tomáš
    The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e. inertial forces are ignored, is shown by time discretization.
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    On the existence of global-in-time weak solutions and scaling laws for Kolmogorovs two-equation model of turbulence
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Mielke, Alexander; Naumann, Joachim
    This paper is concerned with Kolmogorov's two-equation model for free turbulence in space dimension 3, involving the mean velocity u, the pressure p, an average frequency omega, and a mean turbulent kinetic energy k. We first discuss scaling laws for a slightly more general two-equation models to highlight the special role of the model devised by Kolmogorov in 1942. The main part of the paper consists in proving the existence of weak solutions of Kolmogorov's two-equation model under space-periodic boundary conditions in cubes with positive side length l. To this end, we provide new a priori estimates and invoke existence result for pseudo-monotone operators.