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Well-posedness for a generalized derivative nonlinear Schrödinger equation (1601.04167v2)
Published 16 Jan 2016 in math.AP
Abstract: We study the Cauchy problem for a generalized derivative nonlinear Schr\"odinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces $H1$ and $H2$. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space $H1$.