D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 42 Citations 7,723 130 World Ranking 892 National Ranking 51

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Geometry
  • Mechanics

Joachim Escher mainly investigates Mathematical analysis, Degasperis–Procesi equation, Uniqueness, Shallow water equations and Camassa–Holm equation. Joachim Escher merges Mathematical analysis with Large class in his study. As a part of the same scientific family, he mostly works in the field of Degasperis–Procesi equation, focusing on Shock wave and, on occasion, Singularity, Weak solution, Cauchy problem and Mathematical physics.

His work deals with themes such as Motion and Surface tension, which intersect with Uniqueness. In his study, Korteweg–de Vries equation is strongly linked to Peakon, which falls under the umbrella field of Shallow water equations. His study looks at the relationship between Gravitational singularity and topics such as Development, which overlap with Breaking wave, Hunter–Saxton equation, Hyperbolic partial differential equation and Class.

His most cited work include:

  • Wave breaking for nonlinear nonlocal shallow water equations (1086 citations)
  • Global existence and blow-up for a shallow water equation (518 citations)
  • Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation (517 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of investigation include Mathematical analysis, Mechanics, Free boundary problem, Nonlinear system and Boundary value problem. His studies in Mathematical analysis integrate themes in fields like Flow, Exponential stability and Surface tension. His Surface tension study incorporates themes from Gravity, Bounded function and Uniqueness.

His Mechanics research includes elements of Crest and Gravity wave. His biological study spans a wide range of topics, including Harmonic function and Compressibility. His Vorticity study combines topics in areas such as Streamlines, streaklines, and pathlines and Classical mechanics.

He most often published in these fields:

  • Mathematical analysis (69.31%)
  • Mechanics (13.76%)
  • Free boundary problem (13.23%)

What were the highlights of his more recent work (between 2013-2021)?

  • Mathematical analysis (69.31%)
  • Nonlinear system (12.70%)
  • Flow (8.99%)

In recent papers he was focusing on the following fields of study:

Joachim Escher mostly deals with Mathematical analysis, Nonlinear system, Flow, Surface tension and Vorticity. His Parabolic partial differential equation, Free boundary problem and Singularity study in the realm of Mathematical analysis interacts with subjects such as Microelectromechanical systems and Permittivity. His Flow study also includes fields such as

  • Geodesic flow which is related to area like Applied mathematics,
  • Order which intersects with area such as Solving the geodesic equations and Geodesic.

His work in Surface tension addresses subjects such as Bounded function, which are connected to disciplines such as Free surface, Euler's formula, Lubrication and Monotone polygon. His study on Vorticity is covered under Mechanics. His Mechanics study combines topics from a wide range of disciplines, such as Viscosity and Capillary wave.

Between 2013 and 2021, his most popular works were:

  • Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle (46 citations)
  • A Parabolic Free Boundary Problem Modeling Electrostatic MEMS (38 citations)
  • Two-component equations modelling water waves with constant vorticity (35 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Geometry
  • Partial differential equation

His main research concerns Mathematical analysis, Diffeomorphism, Sobolev space, Pure mathematics and Electric potential. His Mathematical analysis research includes themes of Vorticity and Mathematical physics. His Vorticity research incorporates themes from Streamlines, streaklines, and pathlines, Gravity and Integrable system.

The various areas that he examines in his Diffeomorphism study include Norm and Geodesic. His research in Norm tackles topics such as Initial value problem which are related to areas like Euler equations. His research in Harmonic function intersects with topics in Bounded function, Exponential stability and Curvature.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Wave breaking for nonlinear nonlocal shallow water equations

Adrian Constantin;Joachim Escher.
Acta Mathematica (1998)

1170 Citations

Global existence and blow-up for a shallow water equation

Adrian Constantin;Joachim Escher.
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze (1998)

647 Citations

Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation

Adrian Constantin;Joachim Escher.
Communications on Pure and Applied Mathematics (1998)

610 Citations

Particle trajectories in solitary water waves

Adrian Constantin;Joachim Escher.
Bulletin of the American Mathematical Society (2007)

405 Citations

Analyticity of periodic traveling free surface water waves with vorticity

Adrian Constantin;Joachim Escher.
Annals of Mathematics (2011)

388 Citations

Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

Zhaoyang Yin;Olaf Lechtenfeld;Joachim Escher.
Discrete and Continuous Dynamical Systems (2007)

292 Citations

On the blow-up rate and the blow-up set of breaking waves for a shallow water equation

J. Escher;A. Constantin.
Mathematische Zeitschrift (2000)

285 Citations

Global weak solutions and blow-up structure for the Degasperis–Procesi equation

Joachim Escher;Yue Liu;Zhaoyang Yin;Zhaoyang Yin.
Journal of Functional Analysis (2006)

254 Citations

Classical solutions for Hele-Shaw models with surface tension

Joachim Escher;Gieri Simonett.
Advances in Differential Equations (1997)

237 Citations

GLOBAL WEAK SOLUTIONS FOR A SHALLOW WATER EQUATION

Adrian Constantin;Joachim Escher.
Indiana University Mathematics Journal (1998)

191 Citations

Best Scientists Citing Joachim Escher

Adrian Constantin

Adrian Constantin

University of Vienna

Publications: 90

Yue Liu

Yue Liu

The University of Texas at Arlington

Publications: 76

Helge Holden

Helge Holden

Norwegian University of Science and Technology

Publications: 37

Jonatan Lenells

Jonatan Lenells

Royal Institute of Technology

Publications: 35

Jan Prüss

Jan Prüss

Martin Luther University Halle-Wittenberg

Publications: 32

Diego Córdoba

Diego Córdoba

Spanish National Research Council

Publications: 23

Harald Garcke

Harald Garcke

University of Regensburg

Publications: 22

Philippe Laurençot

Philippe Laurençot

Toulouse Mathematics Institute

Publications: 18

Kenneth H. Karlsen

Kenneth H. Karlsen

University of Oslo

Publications: 15

Walter A. Strauss

Walter A. Strauss

Brown University

Publications: 13

Peter W. Michor

Peter W. Michor

University of Vienna

Publications: 12

Yonghong Wu

Yonghong Wu

Curtin University

Publications: 12

Steve Shkoller

Steve Shkoller

University of California, Davis

Publications: 11

Yoshikazu Giga

Yoshikazu Giga

University of Tokyo

Publications: 11

Yong Zhou

Yong Zhou

Nanjing University

Publications: 11

Mingxin Wang

Mingxin Wang

Harbin Institute of Technology

Publications: 10

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

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