| Summary: | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017 === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 175-181). === 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. === by Chenjie Fan. === Ph. D. === Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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