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arXiv · 1711.02388

Local well-posedness for quasi-linear NLS with large Cauchy data on the circle

Roberto Feola·Felice Iandoli
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Abstract

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

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Roberto Feola, Felice Iandoli. 2018-05-16. Local well-posedness for quasi-linear NLS with large Cauchy data on the circle. https://doi.org/10.1016/j.anihpc.2018.04.003

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