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Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in $H^{\frac12}$ (1608.06838v1)
Published 24 Aug 2016 in math.AP
Abstract: We establish the global well-posedness of the derivative nonlinear Schr\"odinger equation with periodic boundary condition in the Sobolev space $H{\frac12}$, provided that the mass of initial data is less than $4\pi$. This result matches the one by Miao, Wu, and Xu and its recent mass threshold improvement by Guo and Wu in the non-periodic setting. Below $H{\frac12}$, we show that the uniform continuity of the solution map on bounded subsets of $Hs$ does not hold, for any gauge equivalent equation.