On the global solutions of quasilinear dispersive equations.

机译：关于拟线性色散方程的整体解。

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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 B1 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.

机译：本文主要研究某些非线性色散方程，其中经典的Picard的不动点参数无法获得所需的局部或整体解。更具体地说，第二章通过短时估计方法用Besov空间B1 2,1中的初始数据证明了圆环T 2上KP-I初始值问题的局部适定性。第三章给出了改进的二维离子Euler-Poisson系统的全局解，假定初始数据是恒定背景的小光滑无旋扰动。证明中的主要成分是准线性I方法，以及分析其时空共振特征的傅立叶变换方法。

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作者
Zhang, Yu.;
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Princeton University.;

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授予单位 Princeton University.;
学科 Mathematics.
学位 Ph.D.
年度 2014
页码 105 p.
总页数 105
原文格式 PDF
正文语种 eng
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8. Theory of Nonlinear Diffusion of Plasma Across a Magnetic Field. I. Solution of a Class of Quasilinear Parabolic Equations. [R] . berryman,james g. 1976

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On the global solutions of quasilinear dispersive equations.

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