The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II

Under the quadratic-decay-conditions of the radial curvatures of an end, we shall derive growth estimates of solutions to the eigenvalue equation and show the absence of eigenvalues.Comment: "$\ge$" in the conditions $(*_4)$ and $(*_5)$ should be replaced by "$>$". $\gamma \ge \frac{n-1}{2}(b-a)$ in the conclusion of Theorem 1.3 should be replaced by $\gamma > \frac{n-1}{2}(b-a)$; trivial miss-calculatio

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system. © 2010 Springer Basel AG

Scattering properties for a pair of Schrödinger type operators on cylindrical domains

Strong asymptotic completeness is shown for a pair of Schr\"{o}dinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre's method within the context of pseudo-selfadjoint operators