- Home
- Best Scientists - Mathematics
- Frank Merle

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
47
Citations
9,698
95
World Ranking
926
National Ranking
48

2020 - Member of Academia Europaea

- Mathematical analysis
- Quantum mechanics
- Geometry

His scientific interests lie mostly in Mathematical analysis, Korteweg–de Vries equation, Mathematical physics, Wave equation and Finite time. His research integrates issues of Universality and Nonlinear system in his study of Mathematical analysis. His work carried out in the field of Korteweg–de Vries equation brings together such families of science as Soliton, Rigidity and Partial differential equation.

He has researched Mathematical physics in several fields, including Vries equation and Conservation law. In his study, Scaling is inextricably linked to Nonlinear phenomena, which falls within the broad field of Vries equation. His Wave equation research incorporates themes from Quantum electrodynamics and Energy.

- On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation (235 citations)
- On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation (235 citations)
- The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation (229 citations)

The scientist’s investigation covers issues in Mathematical analysis, Mathematical physics, Nonlinear system, Wave equation and Soliton. His study in the field of Nonlinear Schrödinger equation, Bounded function and Upper and lower bounds also crosses realms of Finite time. His research in Bounded function tackles topics such as Scaling which are related to areas like Rigidity.

His Mathematical physics research includes elements of Korteweg–de Vries equation, Singularity, Instability and Schrödinger equation. Within one scientific family, Frank Merle focuses on topics pertaining to Heat equation under Nonlinear system, and may sometimes address concerns connected to Sobolev space. His work in Wave equation addresses issues such as Stationary solution, which are connected to fields such as Homogeneous space.

- Mathematical analysis (69.09%)
- Mathematical physics (47.27%)
- Nonlinear system (29.09%)

- Mathematical analysis (69.09%)
- Mathematical physics (47.27%)
- Wave equation (21.82%)

His primary scientific interests are in Mathematical analysis, Mathematical physics, Wave equation, Heat equation and Soliton. His study in Mathematical analysis focuses on Euler equations in particular. His research investigates the connection with Mathematical physics and areas like Anisotropy which intersect with concerns in Symmetry and Combinatorics.

His Wave equation research is multidisciplinary, relying on both Surface, Scaling and Bounded function. His study in Scaling is interdisciplinary in nature, drawing from both Universality, Rigidity, Compact space and Schrödinger equation. His studies in Soliton integrate themes in fields like Space and Schrödinger's cat.

- Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations (33 citations)
- Type II blow up for the energy supercritical NLS (24 citations)
- On strongly anisotropic type I blow up (13 citations)

- Mathematical analysis
- Quantum mechanics
- Geometry

Frank Merle focuses on Mathematical physics, Singularity, Heat equation, Scaling and Bounded function. His Mathematical physics research is multidisciplinary, incorporating elements of Energy and Nonlinear system. His Singularity research is multidisciplinary, incorporating perspectives in Flow and Euler equations.

His Scaling study combines topics from a wide range of disciplines, such as Rigidity, Compact space, Wave equation and Schrödinger equation. To a larger extent, Frank Merle studies Mathematical analysis with the aim of understanding Compact space. In general Mathematical analysis study, his work on Spectral gap often relates to the realm of Implosion, thereby connecting several areas of interest.

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.

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case

Carlos E. Kenig;Frank Merle.

Inventiones Mathematicae **(2006)**

1275 Citations

Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)eu in two dimensions

Haïm Brezis;Frank Merle.

Communications in Partial Differential Equations **(1991)**

813 Citations

Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

Carlos E. Kenig;Frank Merle.

Acta Mathematica **(2008)**

490 Citations

The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

Frank Merle;Pierre Raphaël.

Annals of Mathematics **(2005)**

404 Citations

Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation

Frank Merle;Pierre Raphael.

Journal of the American Mathematical Society **(2003)**

374 Citations

On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation

Frank Merle;Frank Merle;Pierre Raphael.

Inventiones Mathematicae **(2004)**

360 Citations

Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power

F. Merle.

Duke Mathematical Journal **(1993)**

323 Citations

Construction of solutions with exactly $k$ blow-up points for the Schrödinger equation with critical nonlinearity

Frank Merle.

Communications in Mathematical Physics **(1990)**

275 Citations

Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D

F. Merle;L. Vega.

International Mathematics Research Notices **(1998)**

257 Citations

L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity

Frank Merle;Yoshio Tsutsumi.

Journal of Differential Equations **(1990)**

256 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

École Polytechnique

University of Chicago

Université Côte d'Azur

Princeton University

Rutgers, The State University of New Jersey

ETH Zurich

Kyoto University

North Carolina State University

Georgia Institute of Technology

Northwestern University

Wright State University

Dartmouth College

Fitbit (United States)

Northeast Normal University

Chinese Academy of Sciences

University of York

Stowers Institute for Medical Research

University of Barcelona

Scripps Research Institute

University College London

University of Waterloo

University of Maryland, College Park

University of St Andrews

Something went wrong. Please try again later.