Miroslav Bulíček

TL;DR: In this paper, the authors investigated the mathematical properties of internal unsteady three-dimensional flows of such fluids subject to Navier's slip at the boundary and established the long-time existence of a weak solution for large data provided that the viscosity depends on the shear rate and the pressure in a suitably specified manner.

TL;DR: In this paper, Leray et al. considered a complete thermodynamic model for unsteady flows of incompressible homogeneous Newtonian fluids in a fixed bounded three-dimensional domain and established the large-data and long-time existence of weak as well as suitable weak solutions.

TL;DR: This work rigorously investigates the mathematical properties of unsteady three-dimensional internal flows of such incompressible fluids with pressure dependent viscosities and establishes the long-time existence of a (suitable) weak solution when the data are large.

TL;DR: In this paper, the authors consider steady flows of incompressible fluids with power-law-like rheology given by an implicit constitutive equation relating the Cauchy stress and the symmetric part of the velocity gradient in such a way that it leads to a maximal monotone graph.

TL;DR: In this article, implicit constitutive models for elastic solids with limiting small strain have been studied in the context of nonlinear partial differential equations, leading to new classes of challenging mathematical problems.