Abstract
We prove the norm inflation phenomena for the Boussinesq system
on T3 . For arbitrarily small initial data (u0, ρ0) in the negative-order Besov
spaces B˙−1∞,∞ × B˙−1∞,∞, the solution can become arbitrarily large in a short
time. Such largeness can be detected in ρ in Besov spaces of any negative
order: B˙−s∞,∞ for any s > 0.
Original language | English |
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Pages (from-to) | 5449–5463 |
Journal | Discrete and Continuous Dynamical Systems. Series B |
Volume | 26 |
Issue number | 10 |
Online published | Nov 2020 |
DOIs | |
Publication status | Published - Oct 2021 |
Externally published | Yes |
Research Keywords
- Boussinesq system
- norm inflation
- ill-posedness
- negative order Besov spaces
- plane waves