4 papers
Upper bounds on eigenvalue multiplicities for spheres and plane domains revisited
Pierre Bérard, Bernard Helffer
We revisit two papers which appeared in 1999: M.~Hoffmann-Ostenhof, T.~Hoffmann-Ostenhof, and N.~Nadirashvili [Ann. Global Anal. Geom. 17 (1999) 43--48] and T.~Hoff\-mann-Ostenhof,…
On the stability of symmetric flows in a two-dimensional channel
Yaniv Almog, Bernard Helffer
We consider the stability of symmetric flows in a two-dimensional channel (including the Poiseuille flow). In 2015 Grenier, Guo, and Nguyen have established instability of these fl…
Stability of laminar monotone shear flows in a channel for high Reynolds number
Yaniv Almog, Bernard Helffer
We consider the stability of a laminar flow in the two-dimensional channel in the large Reynolds number limit. Assuming that is str…
Cantor spectrum for multidimensional quasi-periodic Schrödinger operators
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
In this paper, we investigate the spectrum of a class of multidimensional quasi-periodic Schrödinger operators that exhibit a Cantor spectrum, which provides a resolution to a que…