About

Carlos Kenig is the Louis Block Distinguished Service Professor in the Department of Mathematics and the College at the University of Chicago. His research focuses on the concentration-compactness and rigidity methods for critical dispersive and wave equations. He has contributed to the understanding of global well-posedness, scattering, and blow-up phenomena for the energy-critical, focusing nonlinear Schrödinger and wave equations. His work involves advanced mathematical techniques to analyze the behavior of solutions to these complex equations, significantly advancing the field of nonlinear partial differential equations.

Research topics

• Mathematics
• Physics
• Quantum mechanics
• Mathematical analysis
• Philosophy
• Law
• Geometry
• Mathematical economics
• Mathematical physics
• Pure mathematics

Selected publications

• Soliton resolution for the radial critical wave equation in all odd space dimensions

  Acta Mathematica · 2023 · 35 citations

  • Mathematics
  • Mathematical analysis
  • Mathematical physics

  Consider the energy-critical focusing wave equation in odd space dimension\n$N\\geq 3$. The equation has a nonzero radial stationary solution $W$, which is\nunique up to scaling and sign change. In this paper we prove that any radial,\nbounded in the energy norm solution of the equation behaves asymptotically as a\nsum of modulated $W$s, decoupled by the scaling, and a radiation term.\n The proof essentially boils down to the fact that the equation does not have\npurely nonradiative multisoliton solutions. The proof overcomes the fundamental\nobstruction for the extension of the 3D case (treated in our previous work,\nCambridge Journal of Mathematics 2013, arXiv:1204.0031) by reducing the study\nof a multisoliton solution to a finite dimensional system of ordinary\ndifferential equations on the modulation parameters. The key ingredient of the\nproof is to show that this system of equations creates some radiation,\ncontradicting the existence of pure multisolitons.\n

  DOI

• Soliton Resolution for Critical Co-rotational Wave Maps and Radial Cubic Wave Equation

  Communications in Mathematical Physics · 2022 · 28 citations

  • Mathematical analysis
  • Mathematics
  • Physics
  DOI

• Elias M. Stein (1931–2018)

  Notices of the American Mathematical Society · 2021

  • Philosophy
  • Mathematical economics
  • Mathematics

  2018) had a profound influence on the field of analysis. He developed tools that are now indispensable, expanded and clarified major theories, and introduced new classes of questions that continue to stimulate research today. In addition, his singular skills as a mentor and expositor left a legacy of dozens of PhD students, hundreds of mathematical descendants, and thousands of loyal readers.

  PublisherDOI

Recent grants

• Harmonic Analysis and Partial Differential Equations

  NSF · $399k · 2005–2010

• Harmonic Analysis and Partial Differential Equations

  NSF · $252k · 2018–2021

• Harmonic Analysis and Partial Differential Equations

  NSF · $296k · 2022–2026

• Harmonic Analysis and Partial Differential Equations

  NSF · $540k · 2013–2019

• Well-Posedness and Long Time Behavior of Some Nonlinear Partial Differential Equations

  NSF · $145k · 2016–2020

Frequent coauthors

• Thomas Duyckaerts

  École Normale Supérieure - PSL

  99 shared

• Luis Vega

  Basque Center for Applied Mathematics

  87 shared

• Gustavo Ponce

  85 shared

• Frank Merle

  CY Cergy Paris Université

  79 shared

• Eugene B. Fabes

  51 shared

• Alexandru D. Ionescu

  Princeton University

  46 shared

• Gigliola Staffilani

  40 shared

• Wilhelm Schlag

  Yale University

  38 shared

Similar researchers at University of Chicago

• Everett E. Vokesh-185
• Ian Fosterh-150
• Jack W. Szostakh-142
• Jean Decetyh-142
• Graeme Bellh-141