Abstract
We consider the equation qt+ qqx= qxx for q: R× (0 , ∞) → H (the quaternions), and show that while singularities can develop from smooth compactly supported data, such situations are non-generic. The singularities will disappear under an arbitrary small “generic” smooth perturbation of the initial data. Similar results are also established for the same equation in S1× (0 , ∞) , where S1 is the standard one-dimensional circle.
Original language | English (US) |
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Pages (from-to) | 41-54 |
Number of pages | 14 |
Journal | Annales Mathematiques du Quebec |
Volume | 46 |
Issue number | 1 |
DOIs | |
State | Published - Apr 2022 |
Bibliographical note
Funding Information:The research of the author was supported in part by grant DMS 1956092 from the National Science Foundation.
Publisher Copyright:
© 2021, Fondation Carl-Herz and Springer Nature Switzerland AG.
Keywords
- Generic well-posedness
- Quaternionic Burgers equation
- Singularities