Navier-Stokes equation solutions
Navier-Stokes equation solutions is a research topic within Applied Mathematics. Science Explorer counts 13k research works in it since 1950. 20.1% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the mathematical modeling and analysis of fluid dynamics, including topics such as Navier-Stokes equations, compressible flows, magnetohydrodynamics, global existence of solutions, weak solutions, boundary value problems, incompressible flow, regularity criteria, and free surface boundary behavior.
- Navier-Stokes Equations
- Compressible Flows
- Magnetohydrodynamics
- Viscous Fluids
- Global Existence
- Weak Solutions
- Boundary Value Problems
- Incompressible Flow
- Regularity Criteria
- Free Surface Boundary
- Research works
- 13k fractional, since 1950
- In the world top 10%
- 2.5k per year above
- Top-10% rate
- 20.1% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +21% the tick is no change
Which countries lead Navier-Stokes equation solutions research?
By volume, China and the United States publish the most (1k and 212 works in 2022–2025).
By volume, 2022–2025
- 1 China 1k works
- 2 United States 212 works
- 3 France 150 works
- 4 Japan 87 works
- 5 Germany 85 works
- 6 Russia 84 works
- 7 Italy 81 works
- 8 South Korea 57 works
- 9 India 56 works
- 10 United Kingdom 43 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Navier-Stokes equation solutions research?
By volume in 2022–2025, Shanghai Jiao Tong University publishes the most Navier-Stokes equation solutions research, followed by Centre National de la Recherche Scientifique and South China University of Technology.
By volume, 2022–2025
- 1 Shanghai Jiao Tong UniversityChina 27 works
- 2 Centre National de la Recherche ScientifiqueFrance 25 works
- 3 South China University of TechnologyChina 19 works
- 4 Academy of Mathematics and Systems ScienceChina 19 works
- 5 Voronezh State UniversityRussia 18 works
- 6 Northwest UniversityChina 17 works
- 7 Institute of Applied Physics and Computational MathematicsChina 17 works
- 8 Czech Academy of Sciences, Institute of MathematicsCzechia 17 works
- 9 Chinese Academy of SciencesChina 17 works
- 10 Fudan UniversityChina 17 works
Who are the leading researchers in Navier-Stokes equation solutions?
The most-cited researchers publishing on Navier-Stokes equation solutions include Stanley Osher, Y. Liu and Tasawar Hayat.
- 1 Stanley Osher United States 8k citations
- 2 Y. Liu France 5.6k citations
- 3 Tasawar Hayat Pakistan 4.6k citations
- 4 Terence Tao United States 3.1k citations
- 5 Miroslav Krstić United States 3.1k citations
- 6 Chi‐Wang Shu United States 2.3k citations
- 7 Liqun Zhang China 2k citations
- 8 Peter D. Lax United States 2k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Navier-Stokes equation solutions research done?
The largest centres of Navier-Stokes equation solutions research in 2022–2025 are Beijing (China), Shanghai (China), Guangzhou (China) and Nanjing (China).
Where is the best place to study Navier-Stokes equation solutions?
Among universities, judged by research, Southwest University, South China University of Technology and Voronezh State University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Southwest UniversityChina | 66.7 | 18.8% | 12.5× | 15 | +480.4% |
| 2 | South China University of TechnologyChina | 65.0 | 19.3% | 8.0× | 19 | +211.2% |
| 3 | Voronezh State UniversityRussia | 57.6 | 7.5% | 80.0× | 18 | +370.8% |
| 4 | Xiamen UniversityChina | 56.6 | 20.4% | 9.6× | 15 | +9.1% |
| 5 | Yonsei UniversitySouth Korea | 52.6 | 24.8% | 5.8× | 9 | +358.2% |
| 6 | Capital Normal UniversityChina | 51.8 | 18.2% | 48.3× | 14 | -26.0% |
| 7 | University of Chinese Academy of SciencesChina | 50.6 | 25.6% | 3.5× | 13 | +820.0% |
| 8 | Guangzhou UniversityChina | 50.6 | 14.4% | 14.9× | 12 | — |
| 9 | Imperial College LondonUnited Kingdom | 49.7 | 33.1% | 4.7× | 9 | +26.3% |
| 10 | South China Normal UniversityChina | 49.2 | 18.9% | 15.0× | 12 | -21.7% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Navier-Stokes equation solutions research growing?
Output in 2018–2022 was 21% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Navier-Stokes equation solutions.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.