Fluid Mixing and Incompressible Optimal Transport

arXiv:2610.09235 · math.OC, cs.SY, eess.SY, physics.flu-dyn · Submitted 2026-10-06 · Read on arXiv

math.OC, cs.SY, eess.SY, physics.flu-dyn

Submitted: 2026-10-06

Updated: 2026-10-06

Comments: 54 pages, 6 figures

Code: https://github.com/johnigraszekcode/Fluid-Mixing-Code

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Optimal Transport — 41× in this paper · explained in 5 episodes
• Gradient Flow — 26× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Homogeneity — 3× in this paper · explained in 2 episodes
• Abundance — 1× in this paper · explained in 1 episode
• Accuracy — 1× in this paper · explained in 1 episode
• Additivity — 1× in this paper · explained in 1 episode
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• The Wasserstein--Ebin Metric: A Geometric Lift of Unbalanced Optimal Transport to the space of Riemannian metrics
• Cellular flow control design for mixing based on the least action principle
• Universal vector and matrix optimal transport
• Some Remarks on Controllability of the Liouville Equation

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