Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in $H^{\frac{1}{2}}$

Abstract

We establish the global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in the Sobolev space $H^{\frac{1}{2}}$, 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 $H^{\frac{1}{2}}$, we show that the uniform continuity of the solution map on bounded subsets of $H^s$ does not hold, for any gauge equivalent equation.

53 pages

References in corpus (1)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data