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Hishida Lab
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The lab uses nonlinear partial differential equations to mathematically uncover the motion of fluids.
AboutAbout the lab
Fluids: a treasure trove of fascinating problems.
The lab of Professor Toshiaki Hishida studies nonlinear partial differential equations, in particular the Navier-Stokes equations, the fundamental equations of fluid dynamics.
Within the physical settings of different domains, such as flow past an object or flow through a gap between walls, the lab seeks to clarify the mathematical properties of the equations and the behavior of their solutions.
In the small classes of the master's program, the topics include the fundamental theory of second-order elliptic equations and the mathematical analysis of stationary and nonstationary problems for the Navier-Stokes equations.
Key terms
- Nonlinear partial differential equations
- Among equations involving rates of change with respect to multiple variables, those whose solutions cannot be built up by simply adding solutions together
- Navier-Stokes equations
- The fundamental equations describing the motion of fluids
- Spatiotemporal asymptotic behavior of solutions
- How a solution behaves as time passes or far away in space
ResearchResearch themes
Focusing on the fundamental equations that describe fluid motion, the lab investigates the mathematical properties of nonlinear partial differential equations. For each domain occupied by the fluid, such as the flow around an object, it seeks to clarify the properties of solutions.
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MembersFaculty
- ProfessorToshiaki Hishida
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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: “F1 CFD Simulation” Cofaser / CC BY-SA 4.0 (cropped)
- Mathematical analysis of fluid equations: “Streamlines around a cylinder” User:Rex the first / Public domain (cropped)
- Related lab (Fourier Analysis and Partial Differential Equations Lab): “Ocean waves water” Jon Sullivan / Public domain (cropped)
- Related lab (Fourier Analysis and Partial Differential Equations Lab): “Unusual wave at the Gap” Avenue / CC BY-SA 3.0 (cropped)
- Related lab (Topology, Differential Geometry, and Global Analysis Lab (Hitoshi Moriyoshi)): “Surface of revolution illustration” Oleg Alexandrov / Public domain (cropped)
- Related lab (Fourier Analysis, Partial Differential Equations, and Fluid Dynamics Lab): “Flow separation” Jaganath at English Wikipedia / CC BY-SA 3.0 (cropped)
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