Global regularity for the energy-critical NLS on ${\mathbb{S}}^3$

Abstract

We establish global existence for the energy-critical nonlinear Schrödinger equation on ${\mathbb{S}}^3$. This follows similar lines to the work on ${\mathbb{T}}^3$ but requires new extinction results for linear solutions and bounds on the first nonlinear iterate at a Euclidean profile that are adapted to the new geometry.

to appear in the Annales IHP, Analyse non lineaire. arXiv admin note: text overlap with arXiv:1102.5771, arXiv:1101.4527

References in corpus (2)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Quintic NLS in the exterior of a strictly convex obstacle