Gustavo Ponce

Q: What Schools Are Affiliated With Gustavo Ponce

Gustavo Ponce is affiliated with the following schools: University of California, Santa Barbara, New York University

Gustavo Ponce's AcademicInfluence.com Rankings

Gustavo Ponce

Mathematics

#601

World Rank

#1122

Historical Rank

Number Theory

#82

World Rank

#116

Historical Rank

Algebra

#101

World Rank

#167

Historical Rank

Measure Theory

#458

World Rank

#654

Historical Rank

mathematics Degrees

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Mathematics

Why Is Gustavo Ponce Influential?

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According to Wikipedia, Gustavo A. Ponce is a Venezuelan mathematician. Education and career Ponce graduated from the Central University of Venezuela with a bachelor's degree in 1976. At the Courant Institute of Mathematical Sciences of New York University he graduated with a master's degree in 1980 and a Ph.D. in 1982 with thesis Long time stability of solutions of nonlinear evolution equations under the supervision of Sergiu Klainerman . Ponce was a visiting lecturer at the University of California, Berkeley from 1982 to 1984, an assistant professor at the Central University of Venezuela from 1984 to 1986, and an assistant professor at the University of Chicago from 1986 to 1989. He was from 1989 to 1991 an associate professor at Pennsylvania State University and is since 1991 a full professor at the University of California, Santa Barbara.

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Gustavo Ponce'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

Commutator estimates and the euler and navier‐stokes equations (1988) (1678)
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle (1993) (1269)
A bilinear estimate with applications to the KdV equation (1996) (782)
Oscillatory integrals and regularity of dispersive equations (1991) (705)
Well-posedness of the initial value problem for the Korteweg-de Vries equation (1991) (617)
Introduction to Nonlinear Dispersive Equations (2009) (470)
On the ill-posedness of some canonical dispersive equations (2001) (401)
The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices (1993) (384)
Global existence of small solutions to a class of nonlinear evolution equations (1985) (322)
Global, small amplitude solutions to nonlinear evolution equations (1983) (261)
Small solutions to nonlinear Schrödinger equations (1993) (244)
Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006) (231)
Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations (1998) (200)
On the global well-posedness of the Benjamin-Ono equation (1991) (185)
Quadratic forms for the 1-D semilinear Schrödinger equation (1996) (160)
The Cauchy problem for quasi-linear Schrödinger equations (2004) (126)
Global stability of large solutions to the 3D Navier-Stokes equations (1994) (124)
On the Zakharov and Zakharov-Schulman Systems (1995) (113)
Local regularity of nonlinear wave equations in three space dimensions (1993) (107)
Well-Posedness of the Euler and Navier-Stokes Equations in the Lebesgue Spaces $L^p_s(\mathbb R^2)$ (1986) (106)
Higher-order nonlinear dispersive equations (1994) (106)
On the Davey-Stewartson systems (1993) (97)
Interaction Equations for Short and Long Dispersive Waves (1998) (96)
Remarks on a paper by J. T. Beale, T. Kato, and A. Majda (1985) (96)
On uniqueness properties of solutions of the k-generalized KdV equations (2006) (91)
On the (generalized) Korteweg-de Vries equation (1989) (91)
On the generalized Benjamin-Ono equation (1994) (87)
On the Ill‐Posedness of the IVP for the Generalized Korteweg‐De Vries and Nonlinear Schrödinger Equations (1996) (85)
Global well-posedness for semi-linear wave equations (2000) (84)
On unique continuation for nonlinear Schrödinger equations (2003) (82)
Uniqueness properties of solutions to Schrödinger equations (2011) (80)
Hardy's uncertainty principle, convexity and Schrödinger evolutions (2008) (74)
Lax Pairs and Higher Order Models for Water Waves (1993) (74)
A model system for strong interaction between internal solitary waves (1992) (73)
The sharp Hardy uncertainty principle for Schrödinger evolutions (2009) (71)
On the Persistent Properties of Solutions to Semi-Linear Schrödinger Equation (2009) (69)
The IVP for the Benjamin-Ono equation in weighted Sobolev spaces (2010) (67)
GLOBAL WELL-POSEDNESS FOR THE MODIFIED KORTEWEG-DE VRIES EQUATION (1999) (60)
Non-uniform continuity in $H\sp 1$ of the solution map of the CH equation (2007) (53)
On the support of solutions to the g-KdV equation (2000) (50)
Dispersive blow-up for nonlinear Schrödinger equations revisited (2013) (50)
On Uniqueness Properties of Solutions of Schrödinger Equations (2006) (49)
Extension and Representation of Divergence-free Vector Fields on Bounded Domains (2000) (48)
WEAK SOLVABILITY AND WELL-POSEDNESS OF A COUPLED SCHRODINGER-KORTEWEG DE VRIES EQUATION FOR CAPILLARY-GRAVITY WAVE INTERACTIONS (1997) (45)
The Navier-Stokes equation with weak initial data (1994) (44)
Nonlinear Small Data Scattering for the Generalized Korteweg-de Vries Equation (1990) (44)
The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces (2011) (42)
The Hardy Uncertainty Principle Revisited (2010) (42)
On the decay properties of solutions to a class of Schr (2007) (42)
Regularity of Solutions to Nonlinear Dispersive Equations (1989) (39)
On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation (2014) (36)
On the Hierarchy of the Generalized KdV Equations (1994) (35)
Global existence for the critical generalized KdV equation (2002) (35)
Variable coefficient Schrödinger flows for ultrahyperbolic operators (2005) (33)
On nonstationary flows of viscous and ideal fluids in $L_{s}^{p}(\mathbb{R}^2)$ (1987) (32)
Global existence of small solutions to the initial value problem for nonlinear thermoelasticity (1990) (31)
The general quasilinear ultrahyperbolic Schrödinger equation (2005) (31)
Convexity properties of solutions to the free Schr (2007) (31)
On the Interaction of Nearly Parallel Vortex Filaments (2003) (30)
On the well-posedness of Benney's interaction equation of short and long waves (1996) (29)
The local ill-posedness of the modified KdV equation (1996) (28)
Decay at infinity of caloric functions within characteristic hyperplanes (2005) (28)
On the propagation of regularities in solutions of the Benjamin-Ono equation (2014) (27)
Breathers and the Dynamics of Solutions in KdV Type Equations (2018) (27)
On Decay Properties of Solutions of the k-Generalized KdV Equation (2012) (27)
Unique continuation properties for solutions to the Camassa-Holm equation and related models (2020) (26)
Decay properties for solutions of fifth order nonlinear dispersive equations (2014) (24)
On persistence properties in fractional weighted spaces (2014) (24)
On the regularity of solutions to a class of nonlinear dispersive equations (2015) (23)
Uncertainty principle of Morgan type and Schrödinger evolutions (2009) (23)
On the Propagation of Regularity of Solutions of the Kadomtsev-Petviashvili Equation (2016) (23)
Well-posedness for the Benney-Roskes/Zakharov- Rubenchik system (2005) (22)
Uniqueness properties of solutions to the Benjamin-Ono equation and related models (2019) (21)
Unique Continuation for Schrödinger Evolutions, with Applications to Profiles of Concentration and Traveling Waves (2010) (21)
On special regularity properties of solutions of the Zakharov-Kuznetsov equation (2018) (20)
Well-posedness for a higher-order Benjamin–Ono equation (2011) (19)
On the Initial Value Problem for the One Dimensional Quasi-Linear Schrödinger Equations (2002) (16)
On the Initial Value Problem for the Ishimori System (2000) (16)
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions (2015) (16)
Global Solutions for the KdV Equation with Unbounded Data (1997) (16)
PROPERTIES OF SOLUTIONS TO THE CAMASSA-HOLM EQUATION ON THE LINE IN A CLASS CONTAINING THE PEAKONS (2016) (15)
On a Class of Solutions to the Generalized Derivative Schrödinger Equations (2017) (15)
On the asymptotic behavior of solutions to the Benjamin-Ono equation (2018) (14)
The initial value problem for a class of nonlinear dispersive equations (1990) (14)
On unique continuation of solutions of Schrödinger equations (2005) (14)
On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation (2016) (13)
On a class of solutions to the generalized KdV type equation (2018) (13)
On a Class of Solutions to the Generalized Derivative Schrödinger Equations (2017) (12)
On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation (2019) (12)
On a Degenerate Zakharov System (2005) (11)
On the unique continuation of solutions to non-local non-linear dispersive equations (2020) (11)
On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces (2010) (11)
A Incompressible ﬂows of an ideal ﬂuid with vorticity in borderline spaces of Besov type (2018) (11)
The non-linear Schrödinger equation with a periodic δ-interaction (2013) (10)
A Theorem of Paley-Wiener Type for Schr\"odinger Evolutions (2012) (8)
Lower bounds for non-trivial travelling wave solutions of equations of KdV type (2011) (7)
Asymptotic Behavior of Solutions of the Dispersion Generalized Benjamin–Ono Equation (2020) (6)
On two dimensional incompressible fluids (1986) (5)
On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation (2015) (4)
Tosio Kato (1917–1999) (2000) (4)
Initial-Boundary Value Problems and the Navier-Stokes Equations (Heinz-Otto Kreiss and Jens Lorenz) (1990) (4)
ON THE WELL POSEDNESS OF THE MODIFIED KORTEWEG-DE VRIES EQUATION IN WEIGHTED SOBOLEV SPACES (2012) (3)
Global existence of solutions to a nonlinear evolution equation with nonlocal coefficients (1987) (3)
On the Stability of Nearly Parallel Vortex Filaments (2006) (3)
On the IVP for the k -Generalized Benjamin–Ono Equation (2016) (3)
Well-posedness results for the dispersion generalized Benjamin-Ono equation via the contraction principle (2012) (3)
PROPAGATION OF REGULARITY AND DECAY OF SOLUTIONS TO NONLINEAR DISPERSIVE EQUATIONS (DRAFT 0) (2022) (2)
Unique Continuation Properties for solutions to the Camassa-Holm equation and other non-local equations (2019) (2)
On Unique Continuation for Non-local Dispersive Models (2021) (2)
Local existence theory for the generalized Schrödinger equation (1997) (1)
The non-linear Schrödinger equation with a periodic δ-interaction (2013) (1)
On Decay Properties of Solutions of the k-Generalized KdV Equation (2013) (1)
Asymptotic Behavior of Solutions for the k-gKdV Equations (2015) (1)
Breathers and the Dynamics of Solutions in KdV Type Equations (2018) (0)
On the regularity of solutions to a class of nonlinear dispersive equations (2016) (0)
Interpolation of Operators: A Multiplier Theorem (2009) (0)
The initial value problem for euler and navier-stokes equations in L s p (ℝ 2 ) (1988) (0)
Asymptotic behavior of solutions of the dispersive generalized Benjamin-Ono equation (2019) (0)
The Nonlinear Schrödinger Equation: Local Theory (2009) (0)
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions (2015) (0)
An Introduction to Sobolev Spaces and Pseudo-Differential Operators (2015) (0)
On persistance properties of the solutions to a class of non linear wave equations (1986) (0)
The Linear Schrödinger Equation (2015) (0)
WELL-POSED NESS OF THE INITIAL VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION (2009) (0)
Lower bounds for the life span of solutions of nonlinear wave equations in higher dimensions (1984) (0)
ON THE WELL POSEDNESS AND ILL POSEDNESS OF THE IVP FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS (Harmonic Analysis and Nonlinear P.D.E.) (2001) (0)
Proceedings of the XV international conference on hyperbolic problems: Theory, numerics, applications (2016) (0)
The Non-Linear Schr\"odinger Equation with a periodic {\bf{$\delta$}}--interaction (2011) (0)
Asymptotic Behavior for k-gKdV Equations (2009) (0)
General Quasilinear Schrödinger Equation (2015) (0)
Propagation of ^{}_{}-smoothness for solutions of the Euler equation (1989) (0)
Asymptotic Behavior of Solutions of the Dispersion Generalized Benjamin–Ono Equation (2020) (0)
On local energy decay for solutions of the Benjamin–Ono equation (2022) (0)
Sobolev Spaces and Pseudo-Differential Operators (2009) (0)
Opening note: third workshop on nonlinear dispersive equations, IMECC-UNICAMP, 2017 (2019) (0)
Asymptotic Behavior for NLS Equation (2009) (0)
A P ] 9 O ct 2 01 9 ON THE LONG TIME BEHAVIOR OF SOLUTIONS TO THE INTERMEDIATE LONG WAVE EQUATION (2019) (0)
The Fourier Transform (2009) (0)
A pr 2 00 6 PERSISTENCE PROPERTIES AND UNIQUE CONTINUATION OF SOLUTIONS OF THE CAMASSA-HOLM EQUATION (0)
The initial value problem for a nonlinear nonuniform parabolic equation (1987) (0)
Asymptotic Behavior of Solutions for the NLS Equation (2015) (0)
Other Nonlinear Dispersive Models (2009) (0)

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What Schools Are Affiliated With Gustavo Ponce?

Gustavo Ponce is affiliated with the following schools:

Gustavo Ponce's Academic­Influence.com Rankings

Why Is Gustavo Ponce Influential?

Gustavo Ponce's Published Works

Published Works

Other Resources About Gustavo Ponce

What Schools Are Affiliated With Gustavo Ponce?

Gustavo Ponce's AcademicInfluence.com Rankings