## Differential and Integral Equations

### On the local ill-posedness of the generalized $p$-Gardner equation

#### Abstract

In this paper, we adapt and extend B. Birnir, G. Ponce, and N. Svanstedt result related with local ill-posedness for the Cauchy problem to the mKdV equation in [5] to the generalized $p$-Gardner equation. We prove that the Cauchy problem for the generalized $2$-Gardner equation is ill-posed in the Sobolev space $H^s(\mathbb{R})$ for $s < -\frac12$.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 11/12 (2014), 1025-1036.

Dates
First available in Project Euclid: 18 August 2014

Quintero, José R.; Arenas-Díaz, Gilberto. On the local ill-posedness of the generalized $p$-Gardner equation. Differential Integral Equations 27 (2014), no. 11/12, 1025--1036. https://projecteuclid.org/euclid.die/1408366783