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Aiki Lab
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The lab mathematically studies the equations that describe the motion of vortices in fluids.

AboutAbout the lab
Examining everyday flows through the lens of mathematics.
The Aiki Lab studies, from a mathematical standpoint, nonlinear partial differential equations that describe natural phenomena such as the flow of water and air, the propagation of sound, and heat conduction.
For partial differential equations that capture the characteristics of these phenomena, the lab investigates whether they can be solved (solvability) and what properties their solutions have.
In particular, the mathematical analysis of model equations describing the motion of vortex filaments, a type of vortex structure that appears in fluid motion, is the core of the lab's research.
This research rigorously treats, in a mathematical way, the foundational theory of model equations related to fluids.
Key terms
- Nonlinear partial differential equation
- A type of mathematical equation that describes complex natural phenomena such as the flow of water and air, the propagation of sound, and heat conduction
- Solvability
- The property of whether an equation can be solved, that is, whether a solution exists. The lab investigates it under a variety of conditions
- Vortex filament
- A type of vortex structure that appears in fluid motion. The equations that model its motion are the lab's object of study
ResearchResearch themes
The Aiki Lab mathematically studies nonlinear partial differential equations that model the motion of fluids, in particular the motion of vortex filaments, a type of vortex structure. Beyond analyzing existing model equations, the lab also works on deriving and mathematically analyzing equations that describe vortex filaments moving in situations that have not been treated before.
View More ↗MembersFaculty
- LecturerMasashi Aiki
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “VortexRingEtna” DavidMPyle / CC BY-SA 4.0 (cropped)
- Analysis of Equations Describing the Motion of Vortex Filaments: “Airplane vortex edit” NASA Langley Research Center (NASA-LaRC), Edited by Fir0002 / Public domain (cropped)
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