Zachary Bradshaw Data-verified
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Associate Professor
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Biography and Research Information
OverviewAI-generated summary
Zachary Bradshaw is an Associate Professor at the University of Arkansas at Fayetteville. His research focuses on the theoretical aspects of fluid dynamics, specifically investigating the Navier-Stokes equations. Bradshaw has explored the existence of global weak solutions and the spatial decay of discretely self-similar solutions to these equations. His work also addresses data assimilation techniques for the Navier-Stokes equations, examining convergence properties of mobile data assimilation schemes using local observables.
Bradshaw's scholarly output includes 58 publications with 168 citations and an h-index of 7. He has been a Principal Investigator (PI) or Co-PI on three federal grants totaling $235,088, including an NSF award of $191,088 for "Separation Rates for Dissipative Nonlinear Partial Differential Equations." He has also co-authored research with Zachary Akridge from the University of Arkansas at Fayetteville.
His recent publications demonstrate an ongoing engagement with the mathematical analysis of fluid flow phenomena. Bradshaw maintains an active laboratory website to share his research activities.
Metrics
- h-index: 7
- Publications: 58
- Citations: 170
Selected Publications
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Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows (2025)
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Asymptotic stability for the 3D Navier-Stokes equations in 𝐿³ and nearby spaces (2025)
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Global Navier-Stokes flows in intermediate spaces (2025)
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Remarks on the separation of Navier–Stokes flows (2024)
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Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations (2023)
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Spatial decay of discretely self-similar solutionsto the Navier–Stokes equations (2023)
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Estimation of non-uniqueness and short-time asymptotic expansions for Navier–Stokes flows (2023)
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Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces (2023)
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Remarks on sparseness and regularity of Navier–Stokes solutions (2022)
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Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space (2022)
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On the Local Pressure Expansion for the Navier–Stokes Equations (2021)
Federal Grants 3 $235,088 total
Separation Rates for Dissipative Nonlinear Partial Differential Equations
Collaboration Network
Top Collaborators
- Existence of global weak solutions to the Navier-Stokes equations in weighted spaces
- On the Local Pressure Expansion for the Navier–Stokes Equations
- Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces
- Local Energy Solutions to the Navier--Stokes Equations in Wiener Amalgam Spaces
- Global Navier-Stokes flows in intermediate spaces
Showing 5 of 7 shared publications
- Spatial decay of discretely self-similar solutionsto the Navier–Stokes equations
- 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
- 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
- Data Assimilation for the Navier--Stokes Equations Using Local Observables
- 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
- Data Assimilation for the Navier--Stokes Equations Using Local Observables
- 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
- Existence of global weak solutions to the Navier-Stokes equations in weighted spaces
- Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space
- The structure of weak solutions to the Navier-Stokes equations
- Remarks on sparseness and regularity of Navier–Stokes solutions
- Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries
- Mild solutions and spacetime integral bounds for Stokes and Navier–Stokes flows in Wiener amalgam spaces
- Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces
- Global Navier-Stokes flows in intermediate spaces
- Global Navier-Stokes flows in intermediate spaces
- Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby 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
- Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows
- Global Weak Solutions of the Navier–Stokes Equations for Intermittent Initial Data in Half-Space
- Time asymptotics, time regularity and separation rates for Navier-Stokes flows in supercritical solution classes
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