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Analysis 1 Lab (Partial Differential Equations, Real Analysis and Functional Analysis, Mathematical Fluid Dynamics; Yasunori Maekawa)
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The lab studies nonlinear equations, with a focus on the Navier-Stokes equations.
AboutAbout the lab
Exploring the mathematical structures hidden in the equations of flow.
The lab studies nonlinear partial differential equations using methods from functional analysis and real analysis.
Centering on the Navier-Stokes equations, the fundamental equations of fluid dynamics, it investigates whether solutions exist and how those solutions behave.
It also studies the various mathematical structures of these equations, such as the dissipation of energy that arises from nonlinear interactions.
Key terms
- Navier-Stokes equations
- Partial differential equations that describe the motion of viscous fluids
- Nonlinear partial differential equations
- Partial differential equations that involve terms such as products of the unknown functions, and for which the principle of superposition does not hold
- Criticality
- A state in an equation in which the strengths of the linear and nonlinear terms are exactly balanced
ResearchResearch themes
The lab studies nonlinear partial differential equations using methods from functional analysis and real analysis. Centering on the Navier-Stokes equations, it investigates the various mathematical structures of these equations.
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MembersFaculty
- ProfessorYasunori Maekawa
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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: “Geodynamo simulation velocity field” Nathanaël Schaeffer / CC BY 4.0 (cropped)
- Properties of Solutions in Critical States: “2011 01 Wirbelst rke 4000” DLR / CC BY 3.0 (cropped)
- Related lab (Analysis 1 (Theory of Partial Differential Equations) Lab (Senjo Shimizu)): “A water droplet collision on a water surface” Subhrajyoti07 / CC BY-SA 4.0 (cropped)
- Related lab (Analysis 2 (Stochastic Analysis, Stochastic Control) Lab (Yushi Hamaguchi)): “Alpha-stable-levy” Thomas Steiner and Martin Keller-Ressel / CC BY-SA 2.5 (cropped)
- Related lab (Analysis 2 (Stochastic Analysis) Lab (Seiichiro Kusuoka)): “Girsanov” Martin Keller-Ressel (uploaded by Thomas Steiner) / CC BY-SA 3.0 (cropped)
- Related lab (Analysis 1 (Real Analysis) Lab (Yohei Tsutsui)): “Fourier Series-Square wave 3 H” Saisundar.s / CC BY-SA 4.0 (cropped)
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