WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN-SIMONS-DIRAC SYSTEM IN TWO DIMENSIONS
WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN-SIMONS-DIRAC SYSTEM IN TWO DIMENSIONS
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二维陈-西蒙斯-狄拉克系统柯西问题的适定性
DOI：
10.1142/s0219891613500276
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发表时间：
2014
影响因子：
0.7
通讯作者：
Mamoru Okamoto
中科院分区：
文献类型：
--
作者：
Junji Koya;Keisuke Kataoka;Takako Kishino-Tauruta;Hiroshi Kobayashi;Kensuke Narukawa;Tomohiko Sato;and Mineo Kurokawa.;Mamoru Okamoto
我们考虑了与1+2中的chen - simons - dirac系统相关的Cauchy问题。利用规范不变性，我们将chen - simons - Dirac系统简化为一个狄拉克方程，并揭示了该狄拉克方程的零结构。接下来，依靠零结构估计，我们建立了与该Dirac方程相关的Cauchy问题在Sobolev空间中是局部时适定的。我们的证明使用改进的l4型估计。
We consider the Cauchy problem associated with the Chern–Simons–Dirac system in ℝ1+2. Using gauge invariance, we reduce the Chern–Simons–Dirac system to a Dirac equation and we uncover the null structure of this Dirac equation. Next, relying on null structure estimates, we establish that the Cauchy problem associated with this Dirac equation is locally-in-time well-posed in the Sobolev space Hsfor all s > 1/4. Our proof uses modified L4-type estimates.