Applied Mathematics Commons^™

Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat

Electronic Theses and Dissertations

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 …