Leaderboards/Navier-Stokes equation solutions

Navier-Stokes equation solutions

Last updated July 7, 2026

Rising Stars

New and hot

Rising Stars Researchers

1
Timothée Crin-Barat
Laboratoire d’Analyse et de Mathématiques Appliquées
2
Thomas Alazard
Centre de Mathématiques Laurent Schwartz
3
Lihua Dong
Nanjing Tech University
4
Young-Pil Choi
Yonsei University
5
Philip Isett
Princeton University
6
Wen Feng
Xi'an Jiaotong University
7
Jiajie Chen
University of Chicago
8
Paolo Antonelli
Gran Sasso Science Institute
9
Roberta Bianchini
Consorzio Roma Ricerche
10
Julien Guillod
Sorbonne Université

Rising Stars Papers

1
On the endpoint regularity in Onsager’sconjecture
Analysis & PDE|2024
25 cit.
2
Stable Nearly Self-Similar Blowup of the 2D Boussinesq and 3D Euler Equations with Smooth Data II: Rigorous Numerics
Multiscale Modeling and Simulation|2025
17 cit.
3
Intermittency and Lower Dimensional Dissipation in Incompressible Fluids
Archive for Rational Mechanics and Analysis|2024
8 cit.
4
Modulated Energy Estimates for Singular Kernels and their Applications to Asymptotic Analyses for Kinetic Equations
SIAM Journal on Mathematical Analysis|2024
6 cit.
5
On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity
Communications in Partial Differential Equations|2024
5 cit.
6
A revisit to the pressureless Euler–Navier–Stokes system in the whole space and its optimal temporal decay
Journal of Differential Equations|2024
5 cit.
7
Virial Theorems and Equipartition of Energy for Water Waves
SIAM Journal on Mathematical Analysis|2024
5 cit.
8
Stability for a System of the 2D Incompressible MHD Equations with Fractional Dissipation
Journal of Mathematical Fluid Mechanics|2024
5 cit.
9
On weak solutions to the kinetic Cucker–Smale model with singular communication weights
Proceedings of the American Mathematical Society|2024
4 cit.
10
Remarks on the smoothness of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> asymptotically self-similar singularity in the 3D Euler and 2D Boussinesq equations
Nonlinearity|2024
4 cit.

Emerging Leaders

Gaining momentum

Emerging Leaders Researchers

1
Weiren Zhao
Zhejiang University
2
Yi Zhu
East China University of Science and Technology
3
In‐Jee Jeong
Korea Institute for Advanced Study
4
Takahito Kashiwabara
Tokyo Institute of Technology
5
Xin Zhong
Southwest University
6
Xin Zhong
Southwest University
7
Xiaoyutao Luo
Institute for Advanced Study
8
Tarek M. Elgindi
Duke University
9
Jianfeng Zhou
Hunan University
10
Xiaoping Zhai
Guangdong Polytechnic of Science and Technology

Emerging Leaders Papers

1
Sharp nonuniqueness for the Navier–Stokes equations
Inventiones mathematicae|2022
69 cit.
2
Stability threshold of two-dimensional Couette flow in Sobolev spaces
Annales de l Institut Henri Poincaré C Analyse Non Linéaire|2022
67 cit.
3
Singularity formation in the incompressible Euler equation in finite and infinite time
EMS Surveys in Mathematical Sciences|2023
49 cit.
4
Stability of the Couette Flow for a 2D Boussinesq System Without Thermal Diffusivity
Archive for Rational Mechanics and Analysis|2022
39 cit.
5
Anomalous Dissipation in Passive Scalar Transport
Archive for Rational Mechanics and Analysis|2022
37 cit.
6
Understanding the broadband near-infrared luminescence in a highly distorted garnet Ca<sub>4</sub>HfGe<sub>3</sub>O<sub>12</sub>:Cr<sup>3+</sup> phosphor
Physical Chemistry Chemical Physics|2023
36 cit.
7
Nonlinear inviscid damping for a class of monotone shear flows in a finite channel
Annals of Mathematics|2024
36 cit.
8
$$L^2$$-Critical Nonuniqueness for the 2D Navier-Stokes Equations
Annals of PDE|2023
26 cit.
9
Global Solutions to 3D Incompressible MHD System with Dissipation in Only One Direction
SIAM Journal on Mathematical Analysis|2023
25 cit.
10
A dynamical approach to the study of instability near Couette flow
Communications on Pure and Applied Mathematics|2023
21 cit.

Current Senior Leaders

Established & currently active

Current Senior Leaders Researchers

1
Zhouping Xin
Chinese University of Hong Kong
2
Edriss S. Titi
University of Cambridge
3
Andrew J. Majda
New York University Abu Dhabi
4
Jiahong Wu
University of Notre Dame
5
Zhifei Zhang
Northwest University
6
Tong Yang
Wuhan University
7
Eitan Tadmor
University of Maryland, College Park
8
Nader Masmoudi
Centre National de la Recherche Scientifique
9
Kevin Zumbrun
Indiana University Bloomington
10
Dehua Wang
University of Pittsburgh

Current Senior Leaders Papers

1
Spectral Methods in Fluid Dynamics.
Mathematics of Computation|1991
3.1k cit.
2
Strong Stability-Preserving High-Order Time Discretization Methods
SIAM Review|2001
2.5k cit.
3
Absorbing boundary conditions for the numerical simulation of waves
Mathematics of Computation|1977
2.4k cit.
4
New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection–Diffusion Equations
Journal of Computational Physics|2000
1.9k cit.
5
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
Communications in Mathematical Physics|1984
1.6k cit.
6
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics|1990
1.2k cit.
7
Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
Communications on Pure and Applied Mathematics|1981
915 cit.
8
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
Communications on Pure and Applied Mathematics|1995
892 cit.
9
Radiation boundary conditions for acoustic and elastic wave calculations
Communications on Pure and Applied Mathematics|1979
754 cit.
10
From particle to kinetic and hydrodynamic descriptions of flocking
Kinetic and Related Models|2008
602 cit.

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