## Differential and Integral Equations

- Differential Integral Equations
- Volume 16, Number 11 (2003), 1281-1291.

### Unique continuation principles for the Benjamin-Ono equation

#### Abstract

Let $\sigma$ denote the Hilbert transform and $\mu\geq0$. We prove that if $u\in C\left( \left[ 0,T\right] ,H^{2}\left( \mathbb{R}\right) \cap L_{2}^{2}\left( \mathbb{R}\right) \right) $ is a solution of \[ \partial_{t}u+2\sigma\partial_{x}^{2}u+u\partial_{x}u=\mu\partial_{x}^{2}u \] such that there are $t_{0} <t_{1}$ $ <t_{2\text{ }}$satisfying $u\left( t_{j}\right) \in H^{4}\left( \mathbb{R}\right) \cap L_{4}^{2}\left( \mathbb{R}\right) $, $j=0,1,2$, then $u\left( t\right) =0$ for all $t\in\left[ 0,T\right] $.

#### Article information

**Source**

Differential Integral Equations, Volume 16, Number 11 (2003), 1281-1291.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060510

**Mathematical Reviews number (MathSciNet)**

MR2016683

**Zentralblatt MATH identifier**

1075.35552

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Secondary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]

#### Citation

Iorio, Rafael José. Unique continuation principles for the Benjamin-Ono equation. Differential Integral Equations 16 (2003), no. 11, 1281--1291. https://projecteuclid.org/euclid.die/1356060510