Space-time estimates for null gauge forms and nonlinear Schrödinger equations. (English) Zbl 1008.35070
Summary: We consider the Cauchy problem for the nonlinear Schrödinger equation in one space dimension with interaction satisfying null gauge condition. We prove the local well-posedness of the problem in the Sobolev space \(H^{1/2}\). The method depends on the nonlinear gauge transformation and on sharp smoothing estimates for the null gauge form.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |