Differential and Integral Equations

On uniqueness for Schrödinger maps with low regularity large data

Ikkei Shimizu

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Abstract

We prove that the solutions to the initial-value problem for the 2-dimensional Schrödinger maps are unique in $$ C_tL^\infty_x \cap L^\infty_t (\dot{H}^1_x\cap\dot{H}^2_x) . $$ For the proof, we follow McGahagan's argument with improving its technical part, combining Yudovich's argument.

Article information

Source
Differential Integral Equations, Volume 33, Number 5/6 (2020), 207-222.

Dates
First available in Project Euclid: 16 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1589594448

Mathematical Reviews number (MathSciNet)
MR4099214

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q60: PDEs in connection with optics and electromagnetic theory 35A02: Uniqueness problems: global uniqueness, local uniqueness, non- uniqueness

Citation

Shimizu, Ikkei. On uniqueness for Schrödinger maps with low regularity large data. Differential Integral Equations 33 (2020), no. 5/6, 207--222. https://projecteuclid.org/euclid.die/1589594448


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