About

Peter Constantin is the John von Neumann Professor in the Department of Mathematics at Princeton University. He is also the Director of PACM at Princeton. His contact information includes the office at Fine Hall, Washington Road, Princeton, NJ, and his email is const-at-math-dot-princeton-dot-edu. The page provides links to his curriculum vitae and lists of publications, including older papers from 2001-2009, papers from 2010-2020, and preprints. No additional biographical or research details are provided on the page.

Research topics

• Mathematics
• Mathematical analysis
• Physics
• Classical mechanics
• Mechanics

Selected publications

• Electroconvection in a magnetic field

  Discrete and Continuous Dynamical Systems · 2026-01-01

  articleOpen access

  Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak solutions with $ L^{\infty} $ data. We show that for strong enough magnetic fields, $ L^{\infty} $-small solutions are smooth globally in time and they obey surface quasigeostrophic equations in the limit of infinite magnetic field strength.

  PublisherOA PDFDOI

• Electric inertia and ideal magnetic reconnection in 2D

  arXiv (Cornell University) · 2026-04-16

  preprintOpen access1st authorCorresponding

  We consider inertial magneto-hydrodynamic systems in 2D. We show global existence and uniqueness of smooth solutions and global existence and uniqueness of weak solutions in Yudovich class. We prove magnetic reconnection without magnetic resistivity, for smooth solutions and for patch solutions. This is obtained by proving merger in corresponding systems of coupled active scalars.

  PublisherDOI

• On putative self-similarity for incompressible 3D Euler

  arXiv (Cornell University) · 2026-02-19

  articleOpen access1st authorCorresponding

  We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent $γ$ which governs the rate of zooming in must be larger than $2/5$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $γ\geq 1/2$. For axisymmetric solutions, we establish the bound $γ\geq 1/2$ in more general settings, including ones in which the outgoing property is not present.

  PublisherOA PDF

• Electric inertia and ideal magnetic reconnection in 2D

  ArXiv.org · 2026-04-16

  articleOpen access1st authorCorresponding

  We consider inertial magneto-hydrodynamic systems in 2D. We show global existence and uniqueness of smooth solutions and global existence and uniqueness of weak solutions in Yudovich class. We prove magnetic reconnection without magnetic resistivity, for smooth solutions and for patch solutions. This is obtained by proving merger in corresponding systems of coupled active scalars.

  PublisherOA PDF

• Shmuel Agmon (1922–2025)

  Notices of the American Mathematical Society · 2026-03-01

  article
  PublisherDOI

• On putative self-similarity for incompressible 3D Euler

  Open MIND · 2026-02-19

  preprint1st authorCorresponding

  We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent $γ$ which governs the rate of zooming in must be larger than $2/5$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $γ\geq 1/2$. For axisymmetric solutions, we establish the bound $γ\geq 1/2$ in more general settings, including ones in which the outgoing property is not present.

  DOI

• Electroconvection in a Magnetic Field

  ArXiv.org · 2025-08-10

  preprintOpen access

  Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak solutions with $L^{\infty}$ data. We show that for strong enough magnetic fields, $L^{\infty}$-small solutions are smooth globally in time and they obey surface quasigeostrophic equations in the limit of infinite magnetic field strength.

  PublisherOA PDFDOI

• Global regularity for critical SQG in bounded domains

  Communications on Pure and Applied Mathematics · 2024-07-24 · 4 citations

  article1st authorCorresponding

  Abstract We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.

  PublisherDOI

• Pressure, Intermittency, Singularity

  arXiv (Cornell University) · 2023-01-11

  preprintOpen access1st authorCorresponding

  We give conditions for regularity of solutions of three dimensional incompressible Navier-Stokes equations based on the pressure and on structure functions.

  PublisherOA PDFDOI

• Magnetic Relaxation of a Voigt–MHD System

  Communications in Mathematical Physics · 2023-06-22 · 15 citations

  article1st author
  PublisherDOI

Recent grants

• Nonlinear Fokker-Planck Equations and Hybrid Stochastic Deterministic Systems

  NSF · $153k · 2011–2013

• Complex and Nonlocal Systems

  NSF · $600k · 2012–2017

• Complex Systems and Boundary Interactions

  NSF · $320k · 2017–2020

• Symmetry, Singularity, and Stability in Fluids and Plasmas

  NSF · $500k · 2021–2026

• FRG: Collaborative Research: Singularities, mixing and long time behavior in nonlinear evolution

  NSF · $252k · 2012–2015

Frequent coauthors

• R. Teman

  40 shared

• Vlad Vicol

  34 shared

• Ciprian Foiaş

  Texas A&M University

  30 shared

• Mihaela Ignatova

  Temple University

  25 shared

• Jiahong Wu

  University of Notre Dame

  24 shared

• B. Nicolaenko

  Texas A&M University

  21 shared

• Edriss S. Titi

  21 shared

• Itamar Procaccia

  Weizmann Institute of Science

  16 shared

Education

• Ph.D

  The Hebrew University of Jerusalem

  1981

• M.A. summa cum laude, Mathematics and Mechanics

  University of Bucharest

  1975

• B.A., Faculty of Mathematics and Mechanics

  University of Bucharest

  1974