Zachary Bradshaw
Affiliation confirmed via AI analysis of OpenAlex, ORCID, and web sources.
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)
Research Areas
Links
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–presentUniversity of Arkansas Department of Mathematical Sciences ORCID
Selected Publications
-
Asymptotic Properties of Discretely Self-Similar Navier–Stokes Solutions with Rough Data (2026)
-
Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows (2025)
-
Asymptotic stability for the 3D Navier-Stokes equations in 𝐿³ and nearby spaces (2025)
-
Global Navier-Stokes flows in intermediate spaces (2025)
-
Remarks on the separation of Navier–Stokes flows (2024)
-
Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations (2023)
-
Spatial decay of discretely self-similar solutions to the Navier–Stokes equations (2023)
-
Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows (2023)
-
Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces (2023)
-
Remarks on sparseness and regularity of Navier–Stokes solutions (2022)
-
Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space (2022)
-
Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries (2021)
-
On the Local Pressure Expansion for the Navier–Stokes Equations (2021)
-
Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations (2020)
-
An Algebraic Reduction of the ‘Scaling Gap’ in the Navier–Stokes Regularity Problem (2018)
Federal Grants 4 $445,088 total
Separation Rates for Dissipative Nonlinear Partial Differential Equations
Collaboration Network
Top Collaborators
- On the Local Pressure Expansion for the Navier–Stokes Equations
- Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations
- Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces
- Global Navier-Stokes flows in intermediate spaces
- Spatial decay of discretely self-similar solutions to the Navier–Stokes equations
- Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows
- Asymptotic Properties of Discretely Self-Similar Navier–Stokes Solutions with Rough Data
- Remarks on sparseness and regularity of Navier–Stokes solutions
- Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries
- An Algebraic Reduction of the ‘Scaling Gap’ in the Navier–Stokes Regularity Problem
- An Algebraic Reduction of the ‘Scaling Gap’ in the Navier–Stokes Regularity Problem
- Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space
- Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space
- Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces
- Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations
- Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations
- Global Navier-Stokes flows in intermediate spaces
- Asymptotic stability for the 3D Navier-Stokes equations in 𝐿³ and nearby spaces
- Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows
Similar Researchers
Based on overlapping research topics