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Topic · Applied Mathematics

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. 10.0% 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%
1.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+16%
the tick is no change
Largest producer
China
55% of the 10 largest, 2022-now
Navier-Stokes equation solutions

Which countries lead Navier-Stokes equation solutions research?

By volume, China and the United States publish the most (1.3k and 271 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.3k works
  2. 2 United States 271 works
  3. 3 France 167 works
  4. 4 Japan 104 works
  5. 5 Germany 101 works
  6. 6 Italy 101 works
  7. 7 Russia 91 works
  8. 8 South Korea 68 works
  9. 9 India 67 works
  10. 10 United Kingdom 58 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: 55.0%United States: 11.9%France: 7.3%Japan: 4.6%6 others listed: 21.3%55%largest
China1,255 · 55.0%United States271 · 11.9%France167 · 7.3%Japan104 · 4.6%6 others listed486 · 21.3%

Shares of the rows listed above, not of the whole node.

Which institutions lead Navier-Stokes equation solutions research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Navier-Stokes equation solutions research, followed by Chinese Academy of Sciences and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 83 works
  2. 2 Chinese Academy of SciencesChina 45 works
  3. 3 Russian Academy of SciencesRussia 39 works
  4. 4 Shanghai Jiao Tong UniversityChina 31 works
  5. 5 South China University of TechnologyChina 22 works
  6. 6 Czech Academy of SciencesCzechia 21 works
  7. 7 Institute of Applied Physics and Computational MathematicsChina 20 works
  8. 8 Fudan UniversityChina 19 works
  9. 9 Southwest UniversityChina 19 works
  10. 10 New York UniversityUnited States 19 works

Who are the leading researchers in Navier-Stokes equation solutions?

The most-cited researchers publishing on Navier-Stokes equation solutions include Xiaogang Wang, Tasawar Hayat and M. Williams.

  1. 1 Xiaogang Wang China 260k citations
  2. 2 Tasawar Hayat Pakistan 135k citations
  3. 3 M. Williams France 134k citations
  4. 4 Jing Li United States 120k citations
  5. 5 Stanley Osher United States 119k citations
  6. 6 Thomas J.R. Hughes United States 106k citations
  7. 7 Y. Liu France 103k citations
  8. 8 Richard S. Ellis United States 97k citations
  9. 9 Giovanni Andrea Prodi Italy 96k citations
  10. 10 Ping Zhang China 83k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Navier-Stokes equation solutions?

The most cited paper in Navier-Stokes equation solutions is "Numerical solution of the Navier-Stokes equations" (ALEXANDRE JOEL CHORIN, 1968), with 5,401 citations. Next come "The numerical simulation of two-dimensional fluid flow with strong shocks" (2,944) and "Systems of conservation laws" (2,682).

Most cited papers
#PaperReleasedCitations
1 Numerical solution of the Navier-Stokes equations ALEXANDRE JOEL CHORIN · Mathematics of Computation 1968 5,401
2 The numerical simulation of two-dimensional fluid flow with strong shocks Paul R. Woodward, Phillip Colella · Journal of Computational Physics Apr 1984 2,944
3 Systems of conservation laws Peter D. Lax, Burton Wendroff · Communications on Pure and Applied Mathematics May 1960 2,682
4 A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws Gary A. Sod · Journal of Computational Physics Open access Apr 1978 2,678
5 Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works Jay P. Boris, David Book · Journal of Computational Physics 1973 2,131
All 98 most cited papers, with filters and sorting

Where is Navier-Stokes equation solutions research done?

The largest centres of Navier-Stokes equation solutions research in 2022-now are Beijing (China), Shanghai (China), Guangzhou (China) and Nanjing (China).

Largest cities, 2022-now

  1. 1 BeijingChina 187 works
  2. 2 ShanghaiChina 108 works
  3. 3 GuangzhouChina 83 works
  4. 4 NanjingChina 74 works
  5. 5 ParisFrance 58 works
  6. 6 WuhanChina 53 works
  7. 7 Xi'anChina 42 works
  8. 8 ZhengzhouChina 41 works
  9. 9 MoscowRussia 37 works
  10. 10 ChongqingChina 37 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, New York University, Chinese University of Hong Kong and Shanghai Jiao Tong 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 18.09%fractional works in this field (log) →share of work in the world top 10% →New York UniversityChinese University o…South China Universi…Shanghai Jiao Tong U…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1New York UniversityUnited States 80.431.7%7.0×19 +57.3%
2Chinese University of Hong KongChina 59.220.6%5.2×9 +21.6%
3Shanghai Jiao Tong UniversityChina 59.19.6%4.6×31 +26.6%
4South China University of TechnologyChina 58.511.8%8.4×22 +32.5%
5Guangdong University of TechnologyChina 58.524.1%8.4×11 +452.8%
6Peking UniversityChina 54.923.1%3.0×15 -1.0%
7Capital Normal UniversityChina 53.59.8%51.4×16 +166.6%
8Imperial College LondonUnited Kingdom 51.122.4%4.1×10 +35.5%
9Xiamen UniversityChina 48.912.3%9.0×18 -13.6%
10University of Chinese Academy of SciencesChina 48.715.5%3.7×14 +13.0%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Navier-Stokes equation solutions, country by country

Is Navier-Stokes equation solutions research growing?

Output in 2022-2025 was 16% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Navier-Stokes equation solutions.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Navier-Stokes equation solutions as a percentage of every work published that year, 0.0097% in 2024.

still counting0.010%0.020%Navier-Stokes equation solutions0.011% in 202519801990200020102020

Fractional works of Navier-Stokes equation solutions over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Navier-Stokes equation solutions9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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