Angkana Rüland, Christian Zillinger and Barbara Zwicknagl Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^lc$) 2017 https://arxiv.org/abs/1709.02880
2016
Angkana Rüland, Christian Zillinger and Barbara Zwicknagl Higher Sobolev regularity of convex integration solutions in elasticity 2016 https://arxiv.org/abs/1610.02529
2015
Christian Zillinger Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity Archive for Rational Mechanics and Analysis 2015 http://link.springer.com/article/10.1007/s00205-016-0991-1
Abstract: In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, (U(y),0), in a periodic channel under Sobolev perturbations. Here, we consider the settings of both an infinite periodic channel of period L, TL×R, as well as a finite periodic channel, TL×[0,1], with impermeable walls. The latter setting is shown to not only be technically more challenging, but to exhibit qualitatively different behavior due to boundary effects.