Quasilinear Schrödinger equations. III: Large data and short time. (Q2065723)

The authors study a class of quasilinear Schrödinger equations where the non-linearity is defined through a positive definite metric \(g\). Earlier well posedness results by the authors [Adv. Math. 231, No. 2, 1151--1172 (2012; Zbl 1248.35196); Kyoto J. Math. 54, No. 3, 529--546 (2014; Zbl 1309.35140)] cover ``small'' initial data with low Sobolev regularity. In the paper under review, the authors consider initial data satisfying a non-trapping condition defined through the metric \(g\), and prove short time local well-posedness in low-regularity Sobolev spaces. In particular, ``large'' initial data are now allowed.