Global wellposedness for a one-dimensional Chern-Simons-Dirac system in L^p
Global wellposedness for a one-dimensional Chern-Simons-Dirac system in L^p
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L^p 中一维 Chern-Simons-Dirac 系统的全局适定性
DOI：
10.1080/03605302.2017.1330339
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Takayoshi
中科院分区：
文献类型：
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作者：
Machihara;Shuji and Ogawa;Takayoshi
讨论了1+1空间和时间维度上的chen - simons - dirac方程在lp (l)上的全局适定性。我们考虑两种类型的二次非线性：零情况和非零情况。我们给出了在flp (f)框架下，当零情况下1≤p≤∞时，chen - simon - dirac方程的时间全局适定性。对于标度临界情况，p= 1时，在考虑时间全局可解性时，可能会出现溶液的质量浓度现象。我们援引德尔加多-坎迪估计，它在防止全球解决方案的集中现象中起着至关重要的作用。我们的方法与Candy（2011）的原始工作有关，他展示了临界空间el2（∈）中具有三次非线性的单Dirac方程的时间全局适定性。
The global wellposedness inLp(ℝ) for the Chern–Simons–Dirac equation in the 1+1 space and time dimension is discussed. We consider two types of quadratic nonlinearity: the null case and the non-null case. We show the time global wellposedness for the Chern–Simon–Dirac equation in the framework ofLp(ℝ), where 1≤p≤∞ for the null case. For the scaling critical case,p= 1, mass concentration phenomena of the solutions may occur in considering the time global solvability. We invoke the Delgado–Candy estimate which plays a crucial role in preventing concentration phenomena of the global solution. Our method is related to the original work of Candy (2011), who showed the time global wellposedness for the single Dirac equation with cubic nonlinearity in the critical spaceL2(ℝ).