Non-uniqueness with forcing for alpha-SQG is established across the full supercritical Sobolev range s < alpha + 2/p, using new smooth compactly supported unstable vortices.
Non-unique weak solutions of forced SQG
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We construct non-unique weak solutions $\theta\in C_t^0C_x^{0-}$ for forced surface quasi-geostrophic (SQG) equation. This is achieved through a convex integration scheme adapted to the sum-difference system of two distinct solutions. Without external forcing, non-unique weak solutions $\theta$ in space $C_t^0C_x^{\alpha}$ with $\alpha<-\frac15$ were constructed by Buckmaster, Shkoller and Vicol, and Isett and Ma.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation
Non-uniqueness with forcing for alpha-SQG is established across the full supercritical Sobolev range s < alpha + 2/p, using new smooth compactly supported unstable vortices.