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arXiv 1202.1967math.AP
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R^{1+1}上Dirac-Klein-Gordon方程的双线性估计及其对整体适定性的应用

Bilinear Estimates and Applications to Global Well-posedness for the Dirac-Klein-Gordon Equation on R^{1+1}

Timothy Candy

摘要:

本文证明了X^{s,b}_ \pm(R^2)空间的新的双线性估计,它们在端点处是最优的.这些估计经常用于R^{1+1}上的非线性狄拉克方程理论。双线性估计的证明遵循陶[21]和D 'Ancona,Foschi和Selberg [11]的精神,从二进分割得到。作为应用,我们利用Colliander,Keel,Staffilani,Takaoka和Tao的I-方法,推广了Tesfahun [23]关于R^{1+1}上Dirac-Klein- Gordon方程在荷类以下整体存在性的工作.

英文摘要:

We prove new bilinear estimates for the X^{s, b}_\pm(R^2) spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on R^{1+1}. The proof of the bilinear estimates follows from a dyadic decomposition in the spirit of Tao [21] and D'Ancona, Foschi, and Selberg [11]. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka, and Tao, we extend the work of Tesfahun [23] on global existence below the charge class for the Dirac-Klein- Gordon equation on R^{1+1}.

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