Vlad Vicol

About

Vlad Vicol is a faculty member at NYU Courant who has been elected to the American Academy of Arts and Sciences. His research focus includes areas related to mathematics, with notable recognition such as the election to the Academy alongside other distinguished faculty members. His contributions have been recognized through awards and honors, indicating a significant impact in his field. Specific details about his research interests, background, or key contributions are not provided in the page text.

Research topics

• Physics
• Mathematics
• Mechanics
• Mathematical analysis

Selected publications

• Formation of Shocks for<scp>2D</scp>Isentropic Compressible Euler

  Communications on Pure and Applied Mathematics · 2020 · 45 citations

  Senior authorCorresponding

  Abstract We consider the 2D isentropic compressible Euler equations, with pressure law p ( ρ ) = (1 γ ) ρ γ , with γ &gt; 1. We provide an elementary constructive proof of shock formation from smooth initial data of finite energy, with no vacuum regions, and with nontrivial vorticity. We prove that for initial data which has minimum slope −1 ε , for ε &gt; 0 taken sufficiently small relative to the amplitude, there exist smooth solutions to the Euler equations which form a shock in time . The bl…

  DOI

• Shock Formation and Vorticity Creation for 3d Euler

  Communications on Pure and Applied Mathematics · 2022 · 39 citations

  Senior authorCorresponding

  Abstract We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direc…

  PublisherDOI

• An intermittent Onsager theorem

  Inventiones mathematicae · 2023-02-26 · 31 citations

  articleSenior author
  PublisherDOI

• Simultaneous Development of Shocks and Cusps for 2D Euler with Azimuthal Symmetry from Smooth Data

  Annals of PDE · 2022-11-19 · 29 citations

  articleSenior authorCorresponding
  PublisherDOI

• Anomalous Diffusion by Fractal Homogenization

  Annals of PDE · 2025-01-03 · 13 citations

  articleOpen accessSenior author
  PublisherOA PDFDOI

Recent grants

• CAREER: Nonlinear stability mechanisms and boundary layer singularities in fluid flows

  NSF · $357k · 2018–2023

• CAREER: Nonlinear stability mechanisms and boundary layer singularities in fluid flows

  NSF · $123k · 2017–2019

• Regularity, stability, and singular limits in fluid dynamics

  NSF · $104k · 2013–2015

Frequent coauthors

• Tristan Buckmaster

  60 shared

• Igor Kukavica

  University of Southern California

  46 shared

• Peter Constantin

  Princeton University

  34 shared

• Steve Shkoller

  University of California, Davis

  29 shared

• Jacob Bedrossian

  22 shared

• Susan Friedlander

  18 shared

• Maria Colombo

  18 shared

• Nathan Glatt-Holtz

  Tulane University

  17 shared

Labs

• Applied Mathematics LaboratoryPI

Awards & honors

• NSF Collaborative Research Grant DMS-2307681
• Simons Investigators program

Similar researchers at New York University

• Jiawei Zhangh-76
• Foster Provosth-60
• Panagiotis Ipeirotish-50