On long time dynamic and singularity formation of NLS

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Fan, Chenjie.

Advisor dc:contributor.advisor

• Gigliola Staffilani.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/112908

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/112908