Abstract
In this paper we consider a Schrödinger equation on the circle with a quadratic nonlinearity. Thanks to an explicit computation of the first Picard iterate, we give a better description of the dynamic of the solution, whose existence was proved by C. E. Kenig, G. Ponce and L. Vega [15]. We also show that the equation is well posed in a space $\mathcal H^{s,p}(\mathbb T)$ which contains the Sobolev space $H^{s}(\mathbb T)$ when $p\geq 2$.
Citation
Laurent Thomann. "Low regularity for a quadratic Schrödinger equation on $\mathbb{T}$." Differential Integral Equations 24 (11/12) 1073 - 1092, November/December 2011. https://doi.org/10.57262/die/1356012877
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