B. Rummler

collaborators

5 papers

math.AP2026

Explicit formulas for gradients and the divergence in n-dimensional spherical coordinates

Bernd Rummler, Gudrun ThÃ¤ter

We use the Laplacian in n-dimensional spherical coordinates (n>1) to write the divergence of a vector field defined on radially symmetric domains in the context of vector calculus.…

math.AP2026

Exact PoincarÃ© Constants in three-dimensional Annuli

Bernd Rummler, Michael Ruzicka, Gudrun ThÃ¤ter

We study 3d-annuli. In our non-dimensional setting each annulus $I^c ◯_{A}$ is defined via two concentrical balls with radii $A /2$ and $A /2 + 1$ . For these geometrie…

math.AP2026

The Stokes Eigenvalue Problem on balls and annuli in three dimensions: Solutions with Poloidal and Toroidal Fields

Bernd Rummler, Gudrun ThÃ¤ter

We consider the Stokes eigenvalue problem in open balls and open annuli in R3 with homogeneous Dirichlet boundary conditions. Using the frame of toroidal and poloidal fields we con…

math.AP2026

Exact Poincare Constants in n-dimensional Annuli

Bernd Rummler, Michael Ruzicka, Gudrun ThÃ¤ter

We study $n$ -dimensional annuli for $n \in {2, \dots, N}$ with $N < \infty$ . We choose a non-dimensional setting such that for any fixed $n$ and given number $A > 0$ the…

math.AP2025

Natural convection in the horizontal annulus: critical Rayleigh number for the steady problem

Arianna Passerini, Bernd Rummler, Michael Ruzicka +1

For the 2D Oberbeck-Boussinesq system in an annulus we are looking for the critical Rayleigh number for which the (nonzero) basic flow loses stability. For this we consider the cor…