# Luis Vega

Spanish mathematician

## Luis Vega 's AcademicInfluence.com Rankings

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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?

(Suggest an Edit or Addition)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 .

## Luis Vega 's Published Works

### 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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