Differential and Integral Equations

Low regularity for a quadratic Schrödinger equation on $\mathbb{T}$

Laurent Thomann

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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 $p\geq 2$.

Article information

Source
Differential Integral Equations, Volume 24, Number 11/12 (2011), 1073-1092.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012877

Mathematical Reviews number (MathSciNet)
MR2866012

Zentralblatt MATH identifier
1249.35312

Subjects
Primary: 35A07 35B35: Stability 35B45: A priori estimates 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Thomann, Laurent. Low regularity for a quadratic Schrödinger equation on $\mathbb{T}$. Differential Integral Equations 24 (2011), no. 11/12, 1073--1092. https://projecteuclid.org/euclid.die/1356012877


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