On singularities in the quaternionic Burgers equation

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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 languageEnglish (US)
Pages (from-to)41-54
Number of pages14
JournalAnnales Mathematiques du Quebec
Volume46
Issue number1
DOIs
StatePublished - 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

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