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Density-dependent incompressible fluids with non-Newtonian viscosity

F. Guillén-González (2004)

Czechoslovak Mathematical Journal

We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of p -coercivity and ( p - 1 ) -growth, for a given parameter p > 1 . The existence of Dirichlet weak solutions was obtained in [2], in the cases p ≥ 12 / 5 if d = 3 or p ≥ 2 if d = 2 , d being the dimension of the domain. In this paper, with help of some new estimates (which lead...

Dependence of fractional powers of elliptic operators on boundary conditions

Pavel E. Sobolevskii (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The realization of an elliptic operator A under suitable boundary conditions is considered and the dependence of the square-root of A from the various conditions is studied.

Derivation of a homogenized two-temperature model from the heat equation

Laurent Desvillettes, François Golse, Valeria Ricci (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...

Derivation of the Reynolds equation for lubrication of a rotating shaft

Antonija Duvnjak, Eduard Marušić-Paloka (2000)

Archivum Mathematicum

In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier–Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed.

Destabilization for quasivariational inequalities of reaction-diffusion type

Vítězslav Babický (2000)

Applications of Mathematics

We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.

Development of small and large compressive pulses in two-phase flow

Nishi Deepa Palo, Jasobanta Jena, Meera Chadha (2024)

Applications of Mathematics

The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss the nonlinear theory of geometrical acoustics. The influence of the solid particles and the rotational...

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