Match tier Confirmed
Presence Current · Arkansas
Last published 2026
Sources OpenAlex · ORCID
Refreshed 2026-10-08

Zachary Bradshaw

Affiliation confirmed via AI analysis of OpenAlex, ORCID, and web sources.

Federal Grant PI

Associate Professor

Also affiliated: University of British Columbia (2014–2017); Virginia Commonwealth University (2009–2014); University of Virginia (2012–2017); University of Maryland, Baltimore County (2023)

10 h-index 52 pubs 282 cited

Biography and Research Information

OverviewAI-generated summary

Zachary Bradshaw's research focuses on the mathematical analysis of partial differential equations, particularly the Navier-Stokes equations that describe fluid motion. His work investigates the theoretical underpinnings of fluid dynamics, exploring concepts such as regularity, scaling, and the existence of solutions in various mathematical spaces.

Bradshaw has authored publications examining the algebraic reduction of the 'scaling gap' in the Navier-Stokes regularity problem, local analyticity radii of solutions, and discretely self-similar solutions. He has also published work on frequency-localized regularity criteria and spatially localized estimates on vorticity. His research has been supported by federal grants from the National Science Foundation (NSF), totaling over $400,000, for projects investigating asymptotic properties of steady Navier-Stokes flows and separation rates for dissipative nonlinear partial differential equations.

His scholarship metrics include an h-index of 7 and 170 total citations across 52 publications. Bradshaw has collaborated with Zachary Akridge from the University of Arkansas at Fayetteville on shared publications. He holds the designation of federal grant principal investigator and maintains an active lab website.

Metrics

  • h-index: 10
  • Publications: 52
  • Citations: 282

Positions

  • Associate Professor 2022–present
    University of Arkansas Department of Mathematical Sciences ORCID

Selected Publications

  • Asymptotic Properties of Discretely Self-Similar Navier–Stokes Solutions with Rough Data (2026)
    SIAM Journal on Mathematical Analysis DOI OpenAlex
  • Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows (2025)
    Journal of Mathematical Fluid Mechanics DOI OpenAlex
  • Asymptotic stability for the 3D Navier-Stokes equations in 𝐿³ and nearby spaces (2025)
    Proceedings of the American Mathematical Society 1 citation DOI OpenAlex
  • Global Navier-Stokes flows in intermediate spaces (2025)
    Journal of Differential Equations 2 citations DOI OpenAlex
  • Remarks on the separation of Navier–Stokes flows (2024)
    Nonlinearity 2 citations DOI OpenAlex
  • Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations (2023)
    Discrete and Continuous Dynamical Systems 5 citations DOI OpenAlex
  • Spatial decay of discretely self-similar solutions to the Navier–Stokes equations (2023)
    Pure and Applied Analysis 6 citations DOI OpenAlex
  • Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows (2023)
    Annales de l Institut Henri Poincaré C Analyse Non Linéaire 1 citation DOI OpenAlex
  • Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces (2023)
    Mathematische Annalen 3 citations DOI OpenAlex
  • Remarks on sparseness and regularity of Navier–Stokes solutions (2022)
    Nonlinearity 4 citations DOI OpenAlex
  • Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space (2022)
    Archive for Rational Mechanics and Analysis 1 citation DOI OpenAlex
  • Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries (2021)
    Transactions of the American Mathematical Society 1 citation DOI OpenAlex
  • On the Local Pressure Expansion for the Navier–Stokes Equations (2021)
    Journal of Mathematical Fluid Mechanics 4 citations DOI OpenAlex
  • Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations (2020)
    Communications in Partial Differential Equations 3 citations DOI OpenAlex
  • An Algebraic Reduction of the ‘Scaling Gap’ in the Navier–Stokes Regularity Problem (2018)
    Archive for Rational Mechanics and Analysis 18 citations DOI OpenAlex

View all publications on OpenAlex →

Federal Grants 4 $445,088 total

NSF Co-PI Oct 2025 - Sep 2026

Conference: The 10th SIAM Central States Section Annual Meeting at the University of Arkansas, October 11-12, 2025

COMPUTATIONAL MATHEMATICS, APPLIED MATHEMATICS $24,000
NSF PI Sep 2026 - Aug 2029

Asymptotic properties of steady Navier-Stokes flows

APPLIED MATHEMATICS $210,000
NSF PI Sep 2023 - Aug 2027

Separation Rates for Dissipative Nonlinear Partial Differential Equations

EPSCoR Co-Funding, APPLIED MATHEMATICS $191,088
NSF Co-PI Apr 2023 - Mar 2025

Conference: Arkansas Spring Lecture Series

ANALYSIS PROGRAM $20,000

Collaboration Network

13 Collaborators 11 Institutions 2 Countries

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