World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
66
Citations
14649
World Ranking
364
National Ranking
16

Research.com Recognitions

  • 2020 - Member of Academia Europaea

Overview

Frank Merle is affiliated with CY Cergy Paris University in France. Their research primarily focuses on various aspects of mathematics, with a significant emphasis on mathematical physics and applied mathematics.

Their work spans multiple advanced topics, including:

  • Advanced Mathematical Physics Problems
  • Stability and Controllability of Differential Equations
  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Nonlinear Dynamics and Pattern Formation
  • Nonlinear Photonic Systems
  • Mathematical Biology Tumor Growth

Frank Merle has contributed to a number of publications in various well-known venues. Frequent publication venues include:

  • arXiv (Cornell University)
  • HAL (Le Centre pour la Communication Scientifique Directe)
  • Archive for Rational Mechanics and Analysis
  • Journal of Differential Equations
  • Discrete and Continuous Dynamical Systems

Recent papers by Frank Merle cover topics related to nonlinear equations and blow-up solutions, showcasing their ongoing interest in the mathematical analysis of evolutionary phenomena:

  • The Blow-Up Rate for a Non-Scaling Invariant Semilinear Heat Equation, 2022, Archive for Rational Mechanics and Analysis
  • Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer-Meinhardt system, 2020, arXiv (Cornell University)
  • A Turing mechanism in order to explain the patchy nature of Crohn's disease, 2021, Journal of Mathematical Biology
  • Blowup solutions for the nonlocal shadow limit model of a singular Gierer-Meinhardt system with critical parameters, 2022, Journal of Differential Equations
  • Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters, 2023, Memoirs of the American Mathematical Society

Collaborative efforts are a notable part of their work, frequently coauthoring with several researchers. Regular collaborators include:

  • Giao Ky Duong
  • Nejla Nouaili
  • Éric Ogier-Denis
  • Mohamed Ali Hamza
  • Nikos I. Kavallaris

The scientist's work bridges theoretical and applied realms, often exploring the stability, dynamics, and controllability of complex differential equations. Their research contributes to an enhanced understanding of nonlinear systems both in physics and biology, tackling problems related to pattern formation, system blow-up behaviour, and mathematical modeling of diseases.

In recognition of their scientific contributions, Frank Merle was named a Member of Academia Europaea in 2020.

Best Publications

  • 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

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

    Haïm Brezis;Frank Merle

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

    Carlos E. Kenig;Frank Merle

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

    Frank Merle;Pierre Raphaël

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

    Frank Merle;Pierre Raphael

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

    Frank Merle;Frank Merle;Pierre Raphael

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

    F. Merle

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

    Frank Merle

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

    F. Merle;L. Vega

  • Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

    Frank Merle;Frank Merle;Pierre Raphael

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

    Frank Merle;Yoshio Tsutsumi

  • Existence of blow-up solutions in the energy space for the critical generalized KdV equation

    Frank Merle

  • A Liouville theorem for the critical generalized Korteweg de Vries equation

    Yvan Martel;Franck Merle;Franck Merle

  • Stability and Asymptotic Stability for Subcritical gKdV Equations

    Yvan Martel;Frank Merle;Tai-Peng Tsai

  • Asymptotic stability of solitons of the subcritical gKdV equations revisited

    Yvan Martel;Franck Merle

  • Instability of solitons for the critical generalized Korteweg—de Vries equation

    Yvan Martel;Franck Merle

  • Classification of the radial solutions of the focusing, energy-critical wave equation

    Thomas Duyckaerts;Carlos Kenig;Frank Merle

  • Stability of the blow-up profile for equations of the type ut=Δu+|u|p−1u

    Frank Merle;Hatem Zaag

  • On Nonexistence of type II blowup for a supercritical nonlinear heat equation

    Hiroshi Matano;Frank Merle

  • Optimal estimates for blowup rate and behavior for nonlinear heat equations

    Frank Merle;Hatem Zaag

Frequent Co-Authors

Yvan Martel
Yvan Martel École Polytechnique
Carlos E. Kenig
Carlos E. Kenig University of Chicago
Pierre Raphaël
Pierre Raphaël Université Côte d'Azur
Igor Rodnianski
Igor Rodnianski Princeton University
Haim Brezis
Haim Brezis Rutgers, The State University of New Jersey
Kenji Nakanishi
Kenji Nakanishi Kyoto University

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

Report an issue

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:

Related Online Degrees & Career Pathways

For students interested in expanding their career options beyond a Mathematics degree, exploring related online degrees can be a smart choice. Many professionals consider MBA programs to gain essential business and leadership skills. Those looking for flexibility should check out online mba accepting transfer credits, which allow students to leverage prior coursework and accelerate their studies.

Data analytics is another promising field closely linked to Mathematics. Pursuing a data analytics masters can open doors in industries like finance, healthcare, and tech, combining mathematical theory with practical insights. Many students also seek out programs that are accessible and easier to get into. Resources highlighting mba programs easy to get into provide valuable guidance on finding graduate options that balance quality with admissions flexibility.

For those prioritizing convenience and remote learning, identifying the easiest online mba program can be essential. These programs often offer streamlined curricula and supportive environments, making them ideal for working professionals or students balancing multiple commitments. Exploring these related paths can enrich a Mathematics background and enhance career prospects.

Best Scientists Citing Frank Merle

Trending Scientists

Recently Published Articles