A semiconvex counterexample to energy monotonicity for time-fractional gradient flows

Marvin Fritz

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arXiv · 2608.01188

A semiconvex counterexample to energy monotonicity for time-fractional gradient flows

Marvin Fritz

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Abstract

For time-fractional gradient flows, natural dissipation statements are often integrated or memory-modified rather than pointwise differential inequalities for the original energy. We construct a smooth, compactly supported, globally semiconvex energy and an absolutely continuous solution on a finite time interval of a time-fractional gradient flow along which the original energy is strictly increasing on an explicit subinterval. The construction incorporates the initial layer directly into the trajectory. After transformation, the curve and its fractional derivative are polynomial, the curve is a regular immersion, and the Hessian remains bounded below up to the anchor.

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Marvin Fritz. 2026-08-02. A semiconvex counterexample to energy monotonicity for time-fractional gradient flows. https://arxiv.org/abs/2608.01188

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