[引用][C] Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations

CE Kenig, G Ponce, L Vega - Inventiones mathematicae, 1998 - Springer
CE Kenig, G Ponce, L Vega
Inventiones mathematicae, 1998Springer
… In this paper we study the local solvability of the IVP (1.1). More precisely, we shall
establish that (1.1) is locally well posed in appropriate Sobolev spaces. … In these particular
cases, the dispersive part of the equation modeled by the operator L does not play any role
in the proof of this local result, see [Kt1], [Kl], [KlPo], [Sh]. Another approach used to
overcome the ``loss of derivatives'' introduced by the …
Consider the initial value problem (IVP) for nonlinear SchroÈdinger equations of the form dtu iLu uYrxuYuYrxu Y t P RY x PR n, u xY0 u0 x Y
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