Term of Award

Spring 2016

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

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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