Ivan Straškraba

Anelastic Approximation as a Singular Limit of the Compressible Navier–Stokes System

Considering compressible Navier–Stokes system in a slab geometry in the regime when both Mach and Froude numbers vanish at the same rate, we study the behavior of corresponding weak solutions, that are known to exist globally-in-time (for large data). We establish their convergence to a solution of the so-called anelastic approximation when the limit flow is stratified, i.e., the limit density depends effectively on the vertical coordinate.

Convergence to equilibria for compressible navier-stokes equations with large data

We show that for any sequence tn→∞ and any global weak solution (ρ(t), u(t)) of barotropic compressible Navier-Stokes equations in 2 and 3 space dimensions with potential force there exists a subsequence {sn} such that ϱ(sn) in Lωr(Ω) of spatially periodic functions, where ϱ∞ is an equilibrium density, r>1 suitable. If the equilibrium is unique then the convergence holds for all t→∞. No smallness of data is assumed.

Power bounded and exponentially bounded matrices

The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.

Global Behavior of Compressible Fluid with a Free Boundary and Large Data

The global behavior of the solutions to one-dimensional Navier-Stokes system with a free boundary is investigated for large data. It is shown that the solutions stabilize to equilibrium in general on subsequences, and completely, if the body force is such that the corresponding equilibrium is unique. Mild condition on state equation is imposed which is satisfied in important physical situations.