兰州大学机构库 >数学与统计学院
KGS-型系统在能量空间中的唯一可解性和爆破
Alternative TitleUnique Solvability and Blow-up in the Energy Space for KGS-type System
石启宏
Thesis Advisor李万同
2015-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
KeywordKGS-型系统 能量解 Strichartz估计 原子空间 唯一可解性 Virial型等式 爆破速率
Abstract本文研究高次作用下的非线性KGS-型系统, 探讨其在能量空间的适定性以及爆破属性等.首先,介绍KGS系统的物理背景、研究现状以及本文研究的问题和所得结果. 此外,证明带有高次非线性项的KGS-型系统能量解存在性,并指出 Yukawa 动量下该解全局存在.其次,考虑具有耗散项的KGS-型系统,证明耗散 KGS-型系统能量解的唯一性和稳定性. 接着,探讨R2+1中的守恒 KGS-型系统.考虑摄动形式的Schrodinger方程,证明在H1 中的非线性势场作用下Schrodinger 方程解的 Kato-型局部光滑估计.进一步,研究R3+1中的守恒KGS-型系统.此外,利用 Littlewood-Paley 分解和嵌入定理得到了非线性项在原子空间的正则性估计. 再通过紧致讨论并结合弱拓扑下的Lipschitz 依赖关系证明了双核子场中的 KGS 系统解的唯一性和关于初值的连续依赖性.最后, 研究高次 Yukawa 作用下的 KGS-型系统,证明了径向解在能量空间的爆破二则性.同时,在假设有限时刻发生爆破的前提下,证明了三维空间中解的爆破速率.
Other AbstractThis thesis is concerned the posedness in the energy space and blow-up attributes for the high-order nonlinear KGS-type systems. First, we give an introduction and prove the existence of the energy solutions for the KGS-type system with higher order nonlinear terms, and point out the solution is global for the system with Yukawa momentum. Second, we prove the uniqueness and stability of the energy solution for KGS-type system with dissipation term. Third, we consider the conserved KGS-type system in R2+1. Schrodinger equation with perturbed Laplace operator is concerned. Then, we study the conserved KGS system in R3+1.Finally, we consider the KGS system and prove the uniqueness and continuous dependence on the initial data. Finally, the higher order Yukawa KGS-type system is discussed. The blow-up alternative for the radial solutions is proved. Furthermore, assuming that blow-up occurs on the finite time, the blow-up rate of the regular solutions in three-dimensional space is obtained.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225690
Collection数学与统计学院
Recommended Citation
GB/T 7714
石启宏. KGS-型系统在能量空间中的唯一可解性和爆破[D]. 兰州. 兰州大学,2015.
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