51 citations · 169 across the 11 of their papers we have counts for
12 papers · 1 filter
On evolutionary problems with a-priori bounded gradients
Miroslav Bulíček, David Hruška, Josef Málek
We study a nonlinear evolutionary partial differential equation that can be viewed as a generalization of the heat equation where the temperature gradient is a~priori bounded but t…
On nonlinear problems of parabolic type with implicit constitutive equations involving flux
Miroslav Bulíček, Josef Málek, Erika Maringová
We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first order divergence operator acting on a flux f…
On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic response
Miroslav Bulíček, Josef Málek, Vít Průša +1
We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fl…
On unsteady flows of pore pressure-activated granular materials
Anna Abbatiello, Miroslav Bulíček, Tomáš Los +2
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in wat…
Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
Michal Bathory, Miroslav Bulíček, Josef Málek
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The flu…
On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion
Jan Blechta, Josef Málek, K. R. Rajagopal
In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy…
On a class of compressible viscoelastic rate-type fluids with stress--diffusion
Miroslav Bulíček, Eduard Feireisl, Josef Málek
We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids with stress diffusion. Our approach is based on the concepts used in the nowadays standar…
On three-dimensional flows of pore pressure activated Bingham fluids
Anna Abbatiello, Tomáš Los, Josef Málek +1
We are concerned with a system of partial differential equations describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (th…
PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion
Miroslav Bulíček, Josef Málek, Vít Průša +1
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonia…
Stress-diffusive regularizations of non-dissipative rate-type materials
Jan Burczak, Josef Málek, Piotr Minakowski
We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mech…
Large data analysis for Kolmogorov's two-equation model of turbulence
Miroslav Bulíček, Josef Málek
We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov's two-equation model of turbulence.…
Unsteady Flows of Fluids with Pressure Dependent Viscosity in Unbounded Domains
Miroslav Bulíček, Mohamed Majdoub, Josef Málek
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the…