Science Explorer Interactive view Map

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. 1 China 1k works
  2. 2 United States 212 works
  3. 3 France 150 works
  4. 4 Japan 87 works
  5. 5 Germany 85 works
  6. 6 Russia 84 works
  7. 7 Italy 81 works
  8. 8 South Korea 57 works
  9. 9 India 56 works
  10. 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.

China: 54.3%United States: 11.3%France: 8.0%Japan: 4.7%6 others listed: 21.7%54%largest
China1,014 · 54.3%United States212 · 11.3%France150 · 8.0%Japan87 · 4.7%6 others listed406 · 21.7%

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.

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. 1 Stanley Osher United States 8k citations
  2. 2 Y. Liu France 5.6k citations
  3. 3 Tasawar Hayat Pakistan 4.6k citations
  4. 4 Terence Tao United States 3.1k citations
  5. 5 Miroslav Krstić United States 3.1k citations
  6. 6 Chi‐Wang Shu United States 2.3k citations
  7. 7 Liqun Zhang China 2k citations
  8. 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).

Largest cities, 2022–2025

  1. 1 Beijing China 156 works
  2. 2 Shanghai China 91 works
  3. 3 Guangzhou China 72 works
  4. 4 Nanjing China 62 works
  5. 5 Paris France 52 works
  6. 6 Wuhan China 44 works
  7. 7 Xi'an China 37 works
  8. 8 Zhengzhou China 36 works
  9. 9 Moscow Russia 33 works
  10. 10 Prague Czechia 32 works
See Navier-Stokes equation solutions on the map

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.

0%20%40%mean 20.1%fractional works in this node (log) →share in the world top 10% →Southwest University: 15, 18.8%South China University of Technology: 19, 19.3%Voronezh State University: 18, 7.5%Xiamen University: 15, 20.4%Yonsei University: 9, 24.8%Capital Normal University: 14, 18.2%University of Chinese Academy of Sciences: 13, 25.6%Guangzhou University: 12, 14.4%Imperial College London: 9, 33.1%South China Normal University: 12, 18.9%Xiamen UniversitySouth China Universi…Southwest UniversityVoronezh State Unive…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Southwest UniversityChina 66.718.8%12.5×15 +480.4%
2 South China University of TechnologyChina 65.019.3%8.0×19 +211.2%
3 Voronezh State UniversityRussia 57.67.5%80.0×18 +370.8%
4 Xiamen UniversityChina 56.620.4%9.6×15 +9.1%
5 Yonsei UniversitySouth Korea 52.624.8%5.8×9 +358.2%
6 Capital Normal UniversityChina 51.818.2%48.3×14 -26.0%
7 University of Chinese Academy of SciencesChina 50.625.6%3.5×13 +820.0%
8 Guangzhou UniversityChina 50.614.4%14.9×12
9 Imperial College LondonUnited Kingdom 49.733.1%4.7×9 +26.3%
10 South China Normal UniversityChina 49.218.9%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.

19801990200020102020
grewheldshrank

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.