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Miura Lab
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The lab studies self-similar structures that appear in nonlinear partial differential equations.
AboutAbout the lab
Self-Similar Structures in Nonlinear Partial Differential Equations
The Miura Lab studies self-similar structures in nonlinear partial differential equations.
Its listed research keywords include the Navier–Stokes equations.
Key terms
- Partial differential equation
- An equation containing rates of change with respect to several variables, such as position and time
- Nonlinear
- The property that the sum of solutions is not necessarily a solution again
- Self-similar
- The property of looking the same in shape after enlargement or reduction. For equations, it refers to solutions that spread while keeping their shape, for example
- Navier–Stokes equations
- Partial differential equations that describe the motion of viscous fluids such as water and air
ResearchResearch themes
*Illustrative imageExistence of Solutions to Fluid Equations
One of the equations describing the motion of vortices in the atmosphere and oceans is the surface quasi-geostrophic (SQG) equation. The lab shows mathematically that, even in a half-plane domain with a boundary, solutions to this equation exist and are determined by the initial state.
MembersFaculty
- ProfessorHideyuki Miura
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: “Yakushima Island Von Karman Vortex street Oct 12 2012” NASA, MODIS Rapid Response System / Public domain (cropped)
- Existence of Solutions to Fluid Equations: “Von Karman Vortex Street Slithers off the Cape Verde Islands (CIRA )” GOES imagery: CSU/CIRA & NOAA / Public domain (cropped)
- Related lab (小野寺研究室): “Minimalfläche mit Seifenhaut Tetraeder 0326” Bin im Garten / CC BY-SA 3.0 (cropped)
- Related lab
(利根川研究室): “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped) - Related lab (本多研究室): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (プルカイト研究室): “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
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