Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 43, Issue 6, Pages 2719-2731Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100792019
Keywords
nonlinear Schrodinger equation; Schrodinger-Poisson system; Schrodinger-Newton system; global well-posedness
Categories
Funding
- JSPS [21.824]
- Grants-in-Aid for Scientific Research [22840039] Funding Source: KAKEN
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We consider the Cauchy problem of the two-dimensional Schrodinger-Poisson system in the energy class. Though the Newtonian potential diverges at spatial infinity in the logarithmic order, global well-posedness is proven in both defocusing and focusing cases. The key is a decomposition of the nonlinearity into a sum of the linear logarithmic potential and a good remainder, which enables us to apply the perturbation method. Our argument can be adapted to the one-dimensional problem.
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