Local and global well-posedness for the Chern-Simons-Dirac system in one dimension

2011/10/28 by Bournaveas, Nikolaos, Candy, Timothy, Machihara, Shuji
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.6345

Abstract

We consider the Cauchy problem for the Chern-Simons-Dirac system on ℝ¹⁺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 L² norm.

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