## Differential and Integral Equations

- Differential Integral Equations
- Volume 19, Number 11 (2006), 1271-1300.

### Low-regularity Schrödinger maps

Alexandru D. Ionescu and Carlos E. Kenig

#### Abstract

We prove that the Schrödinger map initial-value problem \begin{equation*} \begin{cases} & \partial_ts=s\times\Delta_x s\,\text{ on }\,\mathbb{R}^d\times[-1,1];\\ & s(0)=s_0 \end{cases} \end{equation*} is locally well posed for small data $s_0\in H^{{\sigma_0}}_Q(\mathbb{R}^d;\mathbb{S}^2)$, ${\sigma_0}>(d+1)/2$, $Q\in\mathbb{S}^2$.

#### Article information

**Source**

Differential Integral Equations, Volume 19, Number 11 (2006), 1271-1300.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356050302

**Mathematical Reviews number (MathSciNet)**

MR2278007

**Zentralblatt MATH identifier**

1212.35449

**Subjects**

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

#### Citation

Ionescu, Alexandru D.; Kenig, Carlos E. Low-regularity Schrödinger maps. Differential Integral Equations 19 (2006), no. 11, 1271--1300. https://projecteuclid.org/euclid.die/1356050302