Gudrun Thäter

SINGULAR LIMIT OF THE EQUATIONS OF MAGNETOHYDRODYNAMICS IN THE PRESENCE OF STRONG STRATIFICATION

We consider a low Mach, Peclet, Froude and Alfven number limit in the complete Navier–Stokes–Fourier system coupled with Maxwells equations for gases with large specific heat at constant volume. The target system is shown to be the anelastic Oberbeck–Boussinesq system coupled with Maxwells equations. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Lighthill-type equation, from the equations describing the slow fluid flows.

Fractal dimension, attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.

Generalization of the Lorenz model to the two-dimensional convection of second-grade fluids

Abstract We apply the truncation of the Navier–Stokes–Fourier equations which leads to the Lorenz model, to the investigation of second-grade fluids. The new set of equations proves to work as an approximated approach to 2D-convective dynamics, under the same restrictions as for Newtonian fluids. The different behaviour depends only on α 1 and consists in a “modified” Prandtl number.

Theoretical Results on Steady Convective Flows between Horizontal Coaxial Cylinders

For arbitrary Rayleigh number,

Rigorous derivation of the anelastic approximation to the Oberbeck–Boussinesq equations

\mathrm{Ra}

THIRD-GRADE FLUIDS IN THE APERTURE DOMAIN

, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck–Boussinesq system is proved in Theorem 3.5. We show nonlinear stability for large values of the aspect ratio and

Neumann Problem in Domains with Outlets of Bounded Diameter

\mathrm{Ra}<\mathrm{Ra}_L

Steady Flow of a Viscous .Incompressible Fluid in an Unbounded ,(Funnel-Shaped- Domain (*).

, for some number

Imaginary powers of second order differential operators and \(L^q\)-Helmholtz decomposition in the infinite cylinder

\mathrm{Ra}_L

Neumann problem in a perforated layer (sieve)

which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio,