Well-posedness for a generalized derivative nonlinear Schrödinger equation

By M. Hayashi, Tohru Ozawa. 2016

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Abstract We study the Cauchy problem for a generalized derivative nonlinear Schrodinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces H 1 and H 2 . 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 H 1 .

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/082db52396db83ab0be273a19fa25a0433f4b489