Nikolaos Bournaveas, Timothy Candy, Shuji Machihara
Published 2011-10-28Version 1
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.
Almost Optimal Local Well-Posedness of the Chern-Simons-Dirac System in the Coulomb Gauge
Global well-posedness for a NLS-KdV system on $\mathbb{T}$
Global well-posedness of the 3-D full water wave problem
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