Mathematical Research Letters

Volume 19 (2012)

Number 4

Scattering for solutions of NLS in the exterior of a 2D star–shaped obstacle

Pages: 887 – 897



Fabrice Planchon (Laboratoire J. A. Dieudonné, Université de Nice Sophia-Antipolis, Nice, France)

Luis Vega (Departamento de Matemáticas, Universidad del País Vasco, Bilbao, Spain)


We prove that solutions to non-linear Schrödinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non-linear potential is defocusing and grows at least as the quintic power.

2010 Mathematics Subject Classification


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