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Decay and Scattering for the Chern-Simons-Schrodinger Equations

Author(s): Oh, Sung-Jin; Pusateri, Fabio Giuseppe

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Abstract: We consider the Chern-Simons-Schrodinger model in 1 + 2 dimensions, and prove scattering for small solutions of the Cauchy problem in the Coulomb gauge. This model is a gauge covariant Schrodinger equation, with a potential decaying like r(-1) at infinity. To overcome the difficulties due to this long-range decay, we perform L-2-based estimates covariantly. This procedure gives favorable commutation identities so that only curvature terms, which decay faster than r(-1), appear in our weighted energy estimates. We then select the Coulomb gauge to reveal a genuinely cubic null structure, which allows us to establish scattering to linear solutions by Fourier methods.
Publication Date: 2015
Electronic Publication Date: 2-Apr-2015
Citation: Oh, Sung-Jin, Pusateri, Fabio. (2015). Decay and Scattering for the Chern-Simons-Schrodinger Equations. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 13122 - 13147. doi:10.1093/imrn/rnv093
DOI: doi:10.1093/imrn/rnv093
ISSN: 1073-7928
EISSN: 1687-0247
Pages: 13122 - 13147
Type of Material: Journal Article
Version: Author's manuscript

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