One dimensional Dirac equation with quadratic nonlinearities
One dimensional Dirac equation with quadratic nonlinearities
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DOI：
10.3934/dcds.2005.13.277
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发表时间：
2005-04
影响因子：
1.1
通讯作者：
Shuji Machihara
中科院分区：
文献类型：
--
作者：
Shuji Machihara
用两种方法得到了一维具有特殊形式的二次非线性项的非线性Dirac方程的局部适定性。一种是应用Bourgain [2，3]的Fourier限制范数方法，给出非线性项的双线性估计。另一个是研究波动方程的显式解，得到了类似于Bournaveas [4]的双线性估计。
The local well-posedness for the nonlinear Dirac equation with special forms of quadratic nonlinearities in one space dimension is obtained by two approaches. One is to apply the Fourier restriction norm method of Bourgain [2, 3] by showing the bilinear estimates for the nonlinearities. Another is to study the explicit solutions for wave equations and derive another bilinear estimates similar with Bournaveas [4].