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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
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