Quadratic nonlinear derivative Schrödinger equations - Part 2

Bejenaru, Ioan

doi:10.1090/S0002-9947-08-04471-1

Quadratic nonlinear derivative Schrödinger equations - Part 2
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Trans. Amer. Math. Soc. 360 (2008), 5925-5957 Request permission

Abstract:

In this paper we consider the local well-posedness theory for the quadratic nonlinear Schrödinger equation with low regularity initial data in the case when the nonlinearity contains derivatives. We work in $2+1$ dimensions and prove a local well-posedness result for small initial data with low regularity.

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