Frank Merle

Frank Merle's AcademicInfluence.com Rankings

Frank Merle

Mathematics

#7772

World Rank

#10550

Historical Rank

Measure Theory

#2592

World Rank

#3106

Historical Rank

mathematics Degrees

Download Badge

Mathematics

Frank Merle's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Frank Merle Influential?

(Suggest an Edit or Addition)

(See a Problem?)

Frank Merle's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case (2006) (829)
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation (2006) (448)
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation (2005) (306)
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation (2004) (257)
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation (2003) (231)
Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D (1998) (226)
Classification of radial solutions of the focusing, energy-critical wave equation (2012) (195)
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation (2005) (187)
Stability and Asymptotic Stability in the Energy Space of the Sum of N Solitons for Subcritical gKdV Equations (2001) (186)
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009) (167)
Existence of blow-up solutions in the energy space for the critical generalized KdV equation (2001) (164)
Asymptotic stability of solitons of the subcritical gKdV equations revisited (2005) (162)
On Nonexistence of type II blowup for a supercritical nonlinear heat equation (2004) (160)
Optimal estimates for blowup rate and behavior for nonlinear heat equations (1998) (160)
A Liouville theorem for the critical generalized Korteweg–de Vries equation (2000) (157)
Blow up in finite time and dynamics of blow up solutions for the L^2-critical generalized KdV equation (2002) (151)
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation (2004) (147)
Instability of solitons for the critical generalized Korteweg—de Vries equation (2001) (144)
Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions (2007) (140)
Dynamic of Threshold Solutions for Energy-Critical NlS (2007) (133)
ON A SHARP LOWER BOUND ON THE BLOW-UP RATE FOR THE L CRITICAL NONLINEAR SCHRÖDINGER EQUATION (2005) (132)
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications (2008) (126)
Universality of the blow-up profile for small type II blow-up solutions of energy-critical wave equation: the non-radial case (2010) (120)
Dynamic of threshold solutions for energy-critical wave equation (2007) (119)
Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations (2009) (117)
Solution of a nonlinear heat equation with arbitrarily given blow-up points (1992) (116)
Profiles of bounded radial solutions of the focusing, energy-critical wave equation (2012) (116)
Multi solitary waves for nonlinear Schrödinger equations (2006) (114)
Classification of type I and type II behaviors for a supercritical nonlinear heat equation (2009) (109)
Stability of the blow-up profile for equations of the type $u_t=\Delta u+|u|^{p-1}u$ (1997) (106)
A Liouville theorem for vector-valued nonlinear heat equations and applications (2000) (104)
Determination of the blow-up rate for the semilinear wave equation (2003) (101)
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem (2013) (101)
Scattering for radial, bounded solutions of focusing supercritical wave equations (2012) (99)
Determination of the blow-up rate for a critical semilinear wave equation (2005) (98)
Description of two soliton collision for the quartic gKdV equation (2007) (90)
Asymptotic stability of solitons of the gKdV equations with general nonlinearity (2007) (89)
Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton (2014) (89)
On uniqueness and continuation properties after blow‐up time of self‐similar solutions of nonlinear schrödinger equation with critical exponent and critical mass (1992) (86)
Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view (2000) (80)
Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension (2008) (77)
Soliton resolution along a sequence of times for the focusing energy critical wave equation (2016) (73)
Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation (2008) (68)
L2 stability of solitons for KdV equation (2003) (66)
Inelastic interaction of nearly equal solitons for the quartic gKdV equation (2009) (65)
Refined Uniform Estimates at Blow-Up and Applications for Nonlinear Heat Equations (1998) (64)
Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation (2006) (59)
Solutions of the focusing nonradial critical wave equation with the compactness property (2014) (57)
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions (2016) (57)
Blow-up results of viriel type for Zakharov equations (1996) (56)
Threshold and generic type I behaviors for a supercritical nonlinear heat equation (2011) (56)
Blow up for the critical gKdV equation II: minimal mass dynamics (2012) (54)
Blow up for the critical gKdV equation III: exotic regimes (2012) (54)
Stability and Asymptotic Stability for Subcritical gKdV Equations (2002) (53)
Optimal bounds on positive blow-up solutions for a semilinear wave equation (2001) (53)
On the Stability of the Notion of Non-Characteristic Point and Blow-Up Profile for Semilinear Wave Equations (2013) (52)
Stability of Two Soliton Collision for Nonintegrable gKdV Equations (2007) (52)
On growth rate near the blowup surface for semilinear wave equations (2005) (49)
Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System (2007) (48)
Blow up dynamics for smooth equivariant solutions to the energy critical Schr (2011) (47)
Type II blow up for the energy supercritical NLS (2014) (45)
Self-focusing on bounded domains (2001) (42)
Stable Self-Similar Blow-Up Dynamics for Slightly L2 Super-Critical Nls Equations (2009) (40)
Nonexistence of blow-up solution with minimal L2-mass for the critical gKdV equation (2002) (40)
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation (2012) (39)
LOWER BOUNDS FOR THE BLOWUP RATE OF SOLUTIONS OF THE ZAKHAROV EQUATION IN DIMENSION TWO (1996) (35)
Radial solutions to energy supercritical wave equations in odd dimensions (2011) (33)
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schr\"odinger equations (2013) (32)
Description of the Inelastic Collision of Two Solitary Waves for the BBM Equation (2008) (31)
On strongly anisotropic type II blow up (2017) (31)
On the implosion of a three dimensional compressible fluid (2019) (30)
Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5 (2015) (30)
Concentration-compactness and universal profiles for the non-radial energy critical wave equation (2015) (30)
Modulation Theory for the Blowup of Vector-Valued Nonlinear Heat Equations (1995) (29)
Codimension One Threshold Manifold for the Critical gKdV Equation (2015) (27)
Reconnection of vortex with the boundary and finite time quenching (1997) (27)
Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions (2013) (27)
On blow up for the energy super critical defocusing nonlinear Schrödinger equations (2019) (25)
Scattering profile for global solutions of the energy-critical wave equation (2016) (25)
Maximizers for the Strichartz norm for small solutions of mass-critical NLS (2010) (24)
Blow up for the critical gKdV equation I: dynamics near the soliton (2012) (24)
Refined asymptotics around solitons for gKdV equations (2007) (24)
On smooth self similar solutions to the compressible Euler equations (2019) (20)
Inelastic interaction of nearly equal solitons for the BBM equation (2009) (20)
Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem (2011) (20)
Soliton Resolution for Critical Co-rotational Wave Maps and Radial Cubic Wave Equation (2021) (20)
Universality of blow up profile for small blow up solutions to the energy critical wave map equation (2016) (19)
Asymptotics for $L^2$ minimal blow-up solutions of critical nonlinear Schrödinger equation (1996) (18)
ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION (2005) (16)
On the nonexistence of pure multi-solitons for the quartic gKdV equation (2014) (16)
Strongly anisotropic type II blow up at an isolated point (2020) (16)
Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation (2002) (16)
Decay Estimates for Nonradiative Solutions of the Energy-Critical Focusing Wave Equation (2019) (15)
Soliton resolution for the radial critical wave equation in all odd space dimensions (2019) (15)
Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg—de Vries equation (2011) (13)
Exterior Energy Bounds for the Critical Wave Equation Close to the Ground State (2019) (12)
Compactness and single-point blowup of positive solutions on bounded domains (1997) (12)
On collapsing ring blow up solutions to the mass supercritical NLS (2014) (12)
On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles (2022) (12)
Existence and characterization of characteristic points for a semilinear wave equation in one space (2008) (10)
O.D.E. type behavior of blow-up solutions of nonlinear heat equations (2002) (10)
Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation (2008) (10)
On the implosion of a compressible fluid II: Singularity formation (2022) (10)
Inelasticity of soliton collisions for the 5D energy critical wave equation (2017) (9)
Near soliton dynamics and singularity formation for critical problems (2014) (9)
Stability of ODE blow-up for the energy critical semilinear heat equation (2017) (8)
Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schrödinger equation (2019) (8)
Global existence for solutions of the focusing wave equation with the compactness property (2015) (7)
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. (2008) (7)
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders (2006) (6)
Soliton resolution for the radial quadratic wave equation in six space dimensions (2022) (6)
Blow up and near soliton dynamics for the $L^2$ critical gKdV equation (2011) (5)
Uniform Blow-up Estimates for Nonlinear Heat Equations and Applications (2001) (5)
On the energy critical focusing non-linear wave equation (2007) (4)
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem (2012) (4)
A Liouville theorem for the viscous Burgers’s equation (2002) (3)
Stability of blow-up profile for equation of the type (1995) (3)
Blowup Solutions to the Semilinear Wave Equation with a Stylized Pyramid as a Blowup Surface (2016) (2)
On characteristic points at blow-up for a semilinear wave equation in one space dimension (2009) (2)
On classification of non-radiative solutions for various energy-critical wave equations (2022) (2)
On degenerate blow-up profiles for the subcritical semilinear heat equation (2022) (2)
Behavior Rigidity Near Non-Isolated Blow-up Points for the Semilinear Heat Equation (2021) (2)
On channels of energy for the radial linearised energy critical wave equation in the degenerate case (2022) (1)
Erratum to “Asymptotic Stability of Solitons for the Subcritical Generalized KdV Equations” (2002) (1)
Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations (2010) (1)
On the collision of two solitons for the generalized KdV equation in the nonintegrable case (2008) (1)
Optimal control of the growth rate of blow-up solutions of a semilinear wave equation (2021) (0)
Profiles of bounded radial solutions of the focusing, energy-critical wave equation (2012) (0)
Solution to the semilinear wave equation with a pyramid-shaped blow-up surface (2016) (0)
Asymptotics and blow-up for mass critical nonlinear dispersive equations (2017) (0)
A P ] 6 J an 2 01 1 UNIVERSALITY OF THE BLOW-UP PROFILE FOR SMALL TYPE II BLOW-UP SOLUTIONS OF THE ENERGY-CRITICAL WAVE EQUATION : THE NON-RADIAL CASE (2011) (0)
ON THE TRANSVERSAL STABILITY OF SELF SIMILAR BLOW UP FOR THE ENERGY SUPER CRITICAL HEAT EQUATION (2016) (0)
Inelasticity of soliton collisions for the 5D energy critical wave equation (2018) (0)
Uperieure S Ormale N Ecole Stability of Blow-up Proole for Equation of the Type Stability of Blow-up Proole for Equation of the Type (2007) (0)
FOR THE VISCOUS BURGERS'S EQUATION (2002) (0)
A note on a symmetry result for traveling waves in cylinders (2005) (0)
Asymptotics and blow-up for mass critical nonlinear dispersive equations (2017) (0)
Codimension One Threshold Manifold for the Critical gKdV Equation (2015) (0)
Recent progress on the blow-up problem of Zakharov equations (1995) (0)
On blow-up curves for semilinear wave equations (2013) (0)
Multi solitary waves for nonlinear Schrödinger equations Ondes solitaires multiples des équations de Schrödinger nonlinéaires (2006) (0)
Harmonic Analysis and PDEs (2010) (0)
Uperieure S Ormale N Ecole Stability of Blow-up Proole for Equation of the Type Stability of Blow-up Proole for Equation of the Type (2007) (0)
Soliton resolution along a sequence of times for the focusing energy critical wave equation (2017) (0)

This paper list is powered by the following services:

What Schools Are Affiliated With Frank Merle?

Frank Merle is affiliated with the following schools:

CY Cergy Paris University

Frank Merle's Academic­Influence.com Rankings