Term of Award

Spring 2016

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Shijun Zheng

Committee Member 1

Yi Hu

Committee Member 2

Yan Wu

Committee Member 3

Alexander Stokolos

Abstract

In this thesis, we discuss the Gross Pitaevskii Equation (GPE) with harmonic potential and with an angular momentum rotational term in space R^2, which describes the model for Bose-Einstein Condensation. Local Well-Posedness of the equation and the conservation identities for mass, energy and angular momentum are presented. Using the virial identities, we derive the condition for blow-up solution in finite time. Then a threshold of L^2 norm of wave function is obtained for global existence, of GPE in term of ground state solution. This method allows us to obtain our main result ``Sharp sufficient condition for global existence, of NLS with certain in-homogeneous non-linearity". Furthermore, we estimate the universal upper bound for Blow-up rate in super mass critical regime.

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