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Local and global well posedness for the Chern-Simons-Dirac system in one dimension. (English) Zbl 1265.35278
Summary: We consider the Cauchy problem for the Chern-Simons-Dirac system on $$\mathbb {R}^{1+1}$$ with initial data in $$H^s$$. Almost optimal local well posedness is obtained. Moreover, we show that the solution is global in time, provided that initial data for the spinor component has finite charge, or $$L^2$$-norm.

##### MSC:
 35Q41 Time-dependent Schrödinger equations and Dirac equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence
##### Keywords:
Chern-Simons-Dirac system; well posedness; spinor component
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