Zachary Bradshaw Source Confirmed

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

Federal Grant PI

Associate Professor

University of Arkansas at Fayetteville

faculty

7 h-index 57 pubs 167 cited

Research Areas

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OverviewAI-generated summary

Zachary Bradshaw's research focuses on the mathematical analysis of partial differential equations, particularly the Navier-Stokes equations which model fluid flow. His work investigates the existence and properties of solutions to these complex equations, often in specialized mathematical spaces designed to capture specific behaviors of fluid dynamics.

Recent publications explore the spatial decay of solutions in discretely self-similar settings, the existence of global weak solutions in weighted spaces, and the convergence of data assimilation schemes for the 2D Navier-Stokes equations. He has also examined mild solutions and integral bounds in Wiener amalgam spaces, as well as the local pressure expansion and regularity of solutions.

Bradshaw has received federal funding from the National Science Foundation (NSF) for his research. One NSF award of $191,088 supports his work on separation rates for dissipative nonlinear partial differential equations. He has also served as a Co-PI on NSF grants for organizing academic conferences, including the 10th SIAM Central States Section Annual Meeting and the Arkansas Spring Lecture Series. His scholarship metrics include an h-index of 7, 57 total publications, and 167 total citations.

Metrics

h-index: 7
Publications: 57
Citations: 167

Selected Publications

Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows (2025) DOI
Asymptotic stability for the 3D Navier-Stokes equations in 𝐿³ and nearby spaces (2025) DOI
Global Navier-Stokes flows in intermediate spaces (2025) DOI
Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations (2023) DOI
Spatial decay of discretely self-similar solutionsto the Navier–Stokes equations (2023) DOI
Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows (2023) DOI
Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces (2023) DOI
Remarks on sparseness and regularity of Navier–Stokes solutions (2022) DOI
Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space (2022) DOI
On the Local Pressure Expansion for the Navier–Stokes Equations (2021) DOI