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
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.
Recommended Citation
Basharat, Nyla, "Blow-Up Solution and Blow-Up Rate of Bose-Einstein Condensates with Rotational Term" (2016). Electronic Theses and Dissertations. 1377.
https://digitalcommons.georgiasouthern.edu/etd/1377
