## Differential and Integral Equations

- Differential Integral Equations
- Volume 29, Number 1/2 (2016), 183-200.

### On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation

Vladimir Georgiev, Nikolay Tzvetkov, and Nicola Visciglia

#### Abstract

We prove that the solution map associated with the $1D$ half-wave cubic equation in the periodic setting cannot be uniformly continuous on bounded sets of the periodic Sobolev spaces $H^s$ with $s\in ( \frac 14 , \frac 12 )$.

#### Article information

**Source**

Differential Integral Equations, Volume 29, Number 1/2 (2016), 183-200.

**Dates**

First available in Project Euclid: 24 November 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1448323259

**Mathematical Reviews number (MathSciNet)**

MR3450755

**Zentralblatt MATH identifier**

1363.35063

**Subjects**

Primary: 35B65: Smoothness and regularity of solutions 35B20: Perturbations 35B45: A priori estimates

#### Citation

Georgiev, Vladimir; Tzvetkov, Nikolay; Visciglia, Nicola. On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation. Differential Integral Equations 29 (2016), no. 1/2, 183--200. https://projecteuclid.org/euclid.die/1448323259