Frank Merle
#172,980
Most Influential Person Now
Frank Merle's AcademicInfluence.com Rankings
Frank Merlemathematics Degrees
Mathematics
#7772
World Rank
#10550
Historical Rank
Measure Theory
#2592
World Rank
#3106
Historical Rank

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
Why Is Frank Merle Influential?
(Suggest an Edit or Addition)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: