Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp018s45qb99d
 Title: On the global solutions of quasilinear dispersive equations Authors: Zhang, Yu Advisors: Ionescu, Alexandru D Contributors: Mathematics Department Subjects: Mathematics Issue Date: 2014 Publisher: Princeton, NJ : Princeton University Abstract: This thesis mainly focuses on certain nonlinear dispersive equations where the classical Picard's fix-point argument fails in obtaining the desired local or global solutions. More specifically, Chapter two proves the local well-posedness of the KP-I initial value problem on the torus T^2 with initial data in the Besov space B^1_{2,1} through a short-time estimate approach. Chapter three constructs global solutions to a modified ionic Euler-Poisson system in two dimensions, given the initial data is small smooth irrotational perturbation of the constant background. The main ingredients in the proof is a quasi-linear I-method approach, along with the Fourier transform method analyzing its space-time resonance feature. URI: http://arks.princeton.edu/ark:/88435/dsp018s45qb99d Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

Files in This Item:
File Description SizeFormat
Zhang_princeton_0181D_11089.pdf477.97 kBAdobe PDF

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.