## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 48, Number 1 (2019), 207-244.

### Local well-posedness for the derivative nonlinear Schrödinger Equation in Besov Spaces

#### Abstract

It is shown that the cubic derivative nonlinear Schrödinger equation is locally well-posed in Besov spaces $B^{s}_{2,\infty}(\mathbb X)$, $s\ge 1/2$, where we treat the non-periodic setting $\mathbb X=\mathbb R$ and the periodic setting $\mathbb X=\mathbb T$ simultaneously. The proof is based on the strategy of Herr for initial data in $H^{s}(\mathbb T)$, $s\ge 1/2$.

#### Article information

**Source**

Hokkaido Math. J., Volume 48, Number 1 (2019), 207-244.

**Dates**

First available in Project Euclid: 18 February 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1550480650

**Digital Object Identifier**

doi:10.14492/hokmj/1550480650

**Mathematical Reviews number (MathSciNet)**

MR3914175

**Subjects**

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

**Keywords**

local well-posedness derivative nonlinear Schrödinger equation Besov space multilinear estimates

#### Citation

CLOOS, Cai Constantin. Local well-posedness for the derivative nonlinear Schrödinger Equation in Besov Spaces. Hokkaido Math. J. 48 (2019), no. 1, 207--244. doi:10.14492/hokmj/1550480650. https://projecteuclid.org/euclid.hokmj/1550480650