Journal of the European Mathematical Society· 2026Q1
Well-posedness and singularity formation beyond the Yudovich class
- 1citations
- Q1SCImago
- 2026year
Short summary
Researchers introduce a new class of solutions for the 2D Euler equation that allows for unbounded vorticity, proving local existence and uniqueness and demonstrating that these solutions can develop finite-time singularities, exiting the well-posedness class.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduced a local-in-time existence and uniqueness class for 2D Euler equation solutions with unbounded vorticity.
- Demonstrated that solutions in this class can develop finite-time singularities (blow-up).
- Showed that such singular solutions exit the established well-posedness class.
- Proposed studying these singular solutions as a controlled method for investigating singular phenomena.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this class can develop stronger singularities in finite time, meaning that they experience finite time blow-up and exit the well-posedness class. Such solutions may be continued as weak solutions (potentially non-uniquely) after the singularity. While the general dynamics of 2d Euler solutions beyond the Yudovich class will certainly not be so tame, studying such solutions gives a way to study singular phenomena in a more controlled setting.
The authors' abstract, as published at the source. Journal of the European Mathematical Society, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Applied Mathematics
Applied MathematicsMathematics