Monotone Slowdown of Turbulent Flame Speed under Curvature
Curvature is expected to smooth flame-front wrinkles and so reduce turbulent flame speed, and in two-dimensional shear flows this was proved. In three dimensions it fails: there is a smooth periodic shear flow for which introducing Markstein curvature diffusivity increases the effective flame speed predicted by the level-set G-equation.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Partial differential equations
- Posed by
- combustion-theory expectation, proved in 2D by Liu, Xin and Yu
- Year posed
- 2018
- Years open
- 8y
- Solved
- 2026-07-28
- Model
- ChatGPT 5.5 Plus
- Vendor
- OpenAI
- Collaborators
- Hung V. Tran, Jack Xin, Yifeng Yu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
within the curvature G-equation model, in three dimensions
What the AI did
The paper devotes a section titled Exploratory Journey Leading to the Proof to this, and says the model played a significant role in developing the proof. Asked directly about monotonicity, several models including this one took the natural route of differentiating the cell problem and applying a maximum principle, which did not work. Once the authors switched to searching for an example with positive derivative, ChatGPT 5.5 Plus suggested the main formal steps leading to the construction: it helped identify promising ansatzes, organize the linearized calculation, and formulate the orbit-average mechanism showing how a positive value could arise. The authors verified, refined and made the ideas rigorous.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2607.25185 - Turbulent Flame Speed Can Increase under Curvature Smoothing