Luis Vega | Academic Influence

Luis Vega 's AcademicInfluence.com Rankings

Luis Vega

Mathematics

#366

World Rank

#756

Historical Rank

Differential Geometry

#74

World Rank

#88

Historical Rank

Algebra

#79

World Rank

#130

Historical Rank

Geometry

#105

World Rank

#162

Historical Rank

mathematics Degrees

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Mathematics

Luis Vega 's Degrees

PhD Mathematics University of Barcelona
Masters Mathematics University of Barcelona
Bachelors Mathematics University of Barcelona

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Why Is Luis Vega Influential?

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According to Wikipedia, Luis Vega González is a Spanish mathematician, specializing in partial differential equations. Vega graduated from the Complutense University of Madrid with a bachelor's degree in 1982 and received his doctorate in 1988 from Autonomous University of Madrid under Antonio Barba with thesis El multiplicador de Shrödinger la función maximal y los operadores de restriction. Vega was a Dickson Instructor at the University of Chicago as a postdoc. He taught, as an assistant professor, until 1993 at the UAM and then at the University of the Basque Country, where he received a full professorship in 1995. He is the scientific director of the Basque Center for Applied Mathematics .

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Luis Vega '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

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)
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)
Schrödinger equations: pointwise convergence to the initial data (1988) (375)
A bilinear approach to the restriction and Kakeya conjectures (1998) (263)
Small solutions to nonlinear Schrödinger equations (1993) (244)
Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D (1998) (226)
Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations (1998) (200)
Quadratic forms for the 1-D semilinear Schrödinger equation (1996) (160)
Bilinear virial identities and applications (2007) (156)
Schrödinger maximal function and restriction properties of the Fourier transform (1996) (131)
The Cauchy problem for quasi-linear Schrödinger equations (2004) (126)
On the Zakharov and Zakharov-Schulman Systems (1995) (113)
Endpoint Strichartz estimates for the magnetic Schrodinger equation (2009) (110)
Morrey–Campanato Estimates for Helmholtz Equations (1999) (108)
Higher-order nonlinear dispersive equations (1994) (106)
Formation of Singularities and Self-Similar Vortex Motion Under the Localized Induction Approximation (2003) (100)
Non interpolation in Morrey-Campanato and block spaces (1999) (100)
Restriction theorems and maximal operators related to oscillatory integrals in $\mathbb{R}^3$ (1999) (96)
On uniqueness properties of solutions of the k-generalized KdV equations (2006) (91)
On the (generalized) Korteweg-de Vries equation (1989) (91)
A semilinear Dirac equation in H S ( R 3 ) for s >1 (1997) (88)
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)
On local regularity of Schrödinger equations (1993) (84)
Global well-posedness for semi-linear wave equations (2000) (84)
On unique continuation for nonlinear Schrödinger equations (2003) (82)
Global wellposedness for 1D non-linear Schrödinger equation for data with an infinite L2 norm (2001) (81)
Uniqueness properties of solutions to Schrödinger equations (2011) (80)
Almost Everywhere Summability of Fourier Integrals (1988) (75)
Weighted Estimates for the Helmholtz Equation and Some Applications (1997) (75)
Hardy's uncertainty principle, convexity and Schrödinger evolutions (2008) (74)
The sharp Hardy uncertainty principle for Schrödinger evolutions (2009) (71)
Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials (2006) (70)
L2 stability of solitons for KdV equation (2003) (66)
Unique continuation for Schrödinger operators with potential in Morrey spaces (1991) (63)
On the Stability of a Singular Vortex Dynamics (2008) (62)
Shell interactions for Dirac operators (2013) (60)
An analytical proof of Hardy-like inequalities related to the Dirac operator ? (2003) (60)
Carleman inequalities and the heat operator II (2001) (58)
On the existence of maximizers for a family of restriction theorems (2010) (57)
Magnetic virial identities, weak dispersion and Strichartz inequalities (2008) (56)
Schrodinger Maps and Their Associated Frame Systems (2006) (52)
Scattering for 1D cubic NLS and singular vortex dynamics (2009) (51)
On the support of solutions to the g-KdV equation (2000) (50)
Vortex filament equation for a regular polygon (2013) (49)
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and $\delta$-shell interactions (2016) (48)
A real space method for averaging lemmas (2004) (47)
Local regularity of solutions to wave equations with time-dependent potentials (1994) (47)
Spectral stability of Schrödinger operators with subordinated complex potentials (2015) (47)
A NOTE ON THE NONLINEAR SCHRÖDINGER EQUATION IN WEAK Lp SPACES (2001) (45)
Nonlinear Small Data Scattering for the Generalized Korteweg-de Vries Equation (1990) (44)
Shell Interactions for Dirac Operators: On the Point Spectrum and the Confinement (2014) (44)
Existence of maximizers for Sobolev–Strichartz inequalities (2011) (43)
The Hardy Uncertainty Principle Revisited (2010) (42)
The initial value problem for the binormal flow with rough data (2013) (41)
GLOBAL WELLPOSEDNESS FOR 1 D NON-LINEAR SCHRÖDINGER EQUATION FOR DATA WITH AN INFINITE L 2 NORM (2001) (40)
Corrigenda to "Unique continuation for Schrödinger operators" and a remark on intepolation of Morrey spaces (1995) (40)
The Gardner equation and the $L^2$-stability of the $N$-soliton solution of the Korteweg-de Vries equation (2010) (38)
Stability of the Self-similar Dynamics of a Vortex Filament (2012) (36)
Energy Concentration and Sommerfeld Condition for Helmholtz Equation with Variable Index at Infinity (2006) (36)
An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators (2015) (35)
On the Hierarchy of the Generalized KdV Equations (1994) (35)
Some dispersive estimates for Schrödinger equations with repulsive potentials (2006) (33)
Variable coefficient Schrödinger flows for ultrahyperbolic operators (2005) (33)
SELF-ADJOINT EXTENSIONS OF DIRAC OPERATORS WITH COULOMB TYPE SINGULARITY (2012) (32)
Convexity properties of solutions to the free Schr (2007) (31)
The general quasilinear ultrahyperbolic Schrödinger equation (2005) (31)
On the Interaction of Nearly Parallel Vortex Filaments (2003) (30)
On the Dirac delta as initial condition for nonlinear Schrödinger equations (2007) (30)
Spherical Means and Weighted Inequalities (1996) (29)
Decay at infinity of caloric functions within characteristic hyperplanes (2005) (28)
Absence of eigenvalues of two-dimensional magnetic Schrödinger operators (2017) (27)
Evolution of Polygonal Lines by the Binormal Flow (2018) (27)
A Numerical Study of the Self-Similar Solutions of the Schrödinger Map (2008) (26)
Local well-posedness for the modified KdV equation in almost critical $\widehat {H^r_s}$-spaces (2009) (26)
Restriction Theorems and the Schrödinger Multiplier on the Torus (1992) (24)
Uncertainty principle of Morgan type and Schrödinger evolutions (2009) (23)
The forward problem for the electromagnetic Helmholtz equation with critical singularities (2012) (22)
Self-similar solutions of the localized induction approximation: singularity formation (2004) (21)
Unique Continuation for Schrödinger Evolutions, with Applications to Profiles of Concentration and Traveling Waves (2010) (21)
Stability in $L^1$ of circular vortex patches (2009) (21)
HARDY-TYPE ESTIMATES FOR DIRAC OPERATORS (2007) (21)
Uniqueness properties of solutions to the Benjamin-Ono equation and related models (2019) (21)
Self-similar planar curves related to modified Korteweg-de Vries equation (2007) (21)
The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics (2008) (18)
On the local smoothing for the Schrödinger equation (2006) (16)
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions (2015) (16)
Global Solutions for the KdV Equation with Unbounded Data (1997) (16)
Discrete conservation laws and the convergence of long time simulations of the mkdv equation (2011) (16)
On the Initial Value Problem for the Ishimori System (2000) (16)
On the Relationship Between the One-Corner Problem and the M-Corner Problem for the Vortex Filament Equation (2017) (16)
On unique continuation of solutions of Schrödinger equations (2005) (14)
Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces (2007) (14)
The initial value problem for a class of nonlinear dispersive equations (1990) (14)
On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation (2016) (13)
Some weighted Gagliardo-Nirenberg inequalities and applications (2007) (13)
Uniqueness properties for discrete equations and Carleman estimates (2015) (11)
On the equipartition of energy for critical NLW (2008) (11)
Averaging lemmas and the X-ray transform (2003) (11)
Riemann’s Non-differentiable Function and the Binormal Curvature Flow (2020) (10)
Scattering for solutions of NLS in the exterior of a 2d star--shaped obstacle (2011) (10)
Energy concentration and Sommerfeld condition for Helmholtz and Liouville equations (2003) (10)
The dynamics of vortex filaments with corners (2015) (10)
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator (2018) (9)
Weak Dispersive Estimates for Schrödinger Equations with Long Range Potentials (2008) (9)
SELFSIMILAR SOLUTIONS OF THE BINORMAL FLOW AND THEIR STABILITY (2011) (8)
Sommerfeld condition for a Liouville equation and concentration of trajectories (2003) (8)
On the energy of critical solutions of the binormal flow (2019) (8)
A Theorem of Paley-Wiener Type for Schr\"odinger Evolutions (2012) (8)
Unique continuation for the solutions of the laplacian plus a drift (1991) (7)
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion (2019) (7)
Lower bounds for non-trivial travelling wave solutions of equations of KdV type (2011) (7)
Singularity formation for the 1-D cubic NLS and the Schrödinger map on \begin{document}$\mathbb S^2$\end{document} (2018) (7)
On the improvement of the Hardy inequality due to singular magnetic fields (2018) (6)
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation (2018) (6)
Bäcklund transformation and solitonic solutions for a parametric coupled Korteweg-de Vries system (2014) (5)
Bilinear identities involving the k-plane transform and Fourier extension operators (2019) (5)
LOCAL WELL-POSEDNESS FOR THE MODIFIED KDV EQUATION IN ALMOST CRITICAL Ĥ rs-SPACES (2009) (5)
Erratum: “Self-adjoint extensions of Dirac operators with Coulomb type singularity” [J. Math. Phys. 54, 041504 (2013)] (2018) (5)
Carleman type inequalities for fractional relativistic operators (2019) (4)
Asymptotic Lower Bounds for a Class of Schrödinger Equations (2007) (4)
Vortex Filament Equation for a Regular Polygon in the Hyperbolic Plane (2020) (3)
Self-Similar Dynamics for the Modified Korteweg–de Vries Equation (2019) (3)
The Vortex Filament Equation as a Pseudorandom Generator (2013) (3)
Scaling-sharp dispersive estimates for the Korteweg–de Vries group (2008) (3)
Some Lower Bounds for Solutions of Schrödinger Evolutions (2018) (3)
Carleman estimates and necessary conditions for the existence of waveguides (2011) (2)
Relativistic Hardy Inequalities in Magnetic Fields (2013) (2)
Uperieure S Ormale N Ecole Morrey-campanato Estimates for Helmholtz Equation Morrey-campanato Estimates for Helmholtz Equation Morrey-campanato Estimates for Helmholtz Equation (1998) (2)
On the one dimensional cubic NLS in a critical space (2021) (2)
Morrey-Campanato estimates for Helmholtz equation (2021) (2)
Kink solutions of the binormal flow (2003) (1)
Static and dynamical, fractional uncertainty principles (2021) (1)
Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow (2021) (1)
Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system (2014) (1)
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields (2015) (1)
Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ (2017) (1)
Eigenvalue Curves for Generalized MIT Bag Models (2021) (1)
Steady solutions for the Schr\"odinger map equation (2023) (0)
Remarks on global existence and compactness for L 2 solutions of the critical Nonlinear Schrodinger equation in 2D (1998) (0)
A P ] 6 J un 2 00 7 ON THE DIRAC DELTA AS INITIAL CONDITION FOR NONLINEAR SCHRÖDINGER EQUATIONS (2013) (0)
Energy decay and Sommerfeld condition for Helmholtz equation with variable index at in nity (2021) (0)
WELL-POSED NESS OF THE INITIAL VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION (2009) (0)
On the integrability of evolving membranes (2015) (0)
J an 2 00 7 SCHRÖDINGER MAPS AND THEIR ASSOCIATED FRAME SYSTEMS (2019) (0)
Stability of the Self-similar Dynamics of a Vortex Filament (2013) (0)
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions (2015) (0)
New Conservation Laws and Energy Cascade for 1d Cubic NLS and the Schr\"odinger map (2023) (0)
On the Relationship Between the One-Corner Problem and the M-Corner Problem for the Vortex Filament Equation (2018) (0)
Relativistic Hardy Inequalities in Magnetic Fields (2014) (0)
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields (2014) (0)
On the Local Smoothing for the Schroedinger Equation (2006) (0)
The Evolution of the Local Induction Approximation for a Regular Polygon (2014) (0)
Blow-up for the 1D cubic NLS (2023) (0)

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