Abstract
We demonstrate norm inflation for nonlinear nonlocal equations, which extend the Korteweg-de Vries equation to permit fractional dispersion, in the periodic and non-periodic settings. That is, an initial datum is smooth and arbitrarily small in a Sobolev space but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 833-850 |
| Number of pages | 18 |
| Journal | Differential and Integral Equations |
| Volume | 31 |
| Issue number | 11-12 |
| DOIs | |
| State | Published - Nov 2018 |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics