Global well-posedness of NLS with a rough potential below the energy norm
classification
🧮 math.AP
keywords
potentialroughanalysisapproachbelowcalledcolliander-keel-staffilani-takaoka-taocubic
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We show that in the presence of a rough external potential, a 3d cubic defocusing NLS is globally well-posed in H^s for s>5/6. The proof is based on the approach of Colliander-Keel-Staffilani-Takaoka-Tao, called the I-method, but in order to deal with a rough potential, we modify harmonic analysis tools by spectral theory.
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