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arXiv · 2003.04815

Local well-posedness for the quasi-linear Hamiltonian Schr\"odinger equation on tori

Roberto Feola·Felice Iandoli
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Abstract

We prove a local in time well-posedness result for quasi-linear Hamiltonian Schr\"odinger equations on $\mathbb{T}^d$ for any $d\geq 1$. For any initial condition in the Sobolev space $H^s$, with $s$ large, we prove the existence and unicity of classical solutions of the Cauchy problem associated to the equation. The lifespan of such a solution depends only on the size of the initial datum. Moreover we prove the continuity of the solution map.

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Roberto Feola, Felice Iandoli. 2020-03-10. Local well-posedness for the quasi-linear Hamiltonian Schr\"odinger equation on tori. https://doi.org/10.1016/j.matpur.2021.11.009

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