Monotone Slowdown of Turbulent Flame Speed under Curvature
Statement
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.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Hung V. Tran, Jack Xin and Yifeng Yu, using ChatGPT 5.5 PlusThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.