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On long time dynamic and singularity formation of NLS

Author(s)
Fan, Chenjie.
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Download1015202726-MIT.pdf (8.022Mb)
Alternative title
On long time dynamic and singularity formation of nonlinear Schrödinger equation
Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Gigliola Staffilani.
Terms of use
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
In this thesis, we investigate the long time behavior of focusing mass critical nonlinear Schrödinger equation (NLS). We will focus on the singularity formation and long time asymptotics. To be specific, there are two parts in the thesis. In the first part, we give a construction of log-log blow up solutions which blow up at m prescribed points simultaneously. In the second part, we show weak convergence to ground state for certain radial blow up solutions to NLS at well chosen time sequence. We also include a lecture note on concentration compactness. Concentration compactness is one of the main tool we use in the second part of the thesis.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 175-181).
 
Date issued
2017
URI
http://hdl.handle.net/1721.1/112908
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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