Zachary Bradshaw
Contact
Information
Department of Mathematics
University of British Columbia
E-mail: zbradshaw@math.ubc.ca
Research
Interests
Mathematical Fluid Dynamics and Partial Differential Equations. In particular,
• singularity formation and regularity in the 3D Navier-Stokes equations and related models,
• rigorous theories of turbulence and transport in fluids and plasmas
Professional
Development
University of British Columbia
Postdoctoral research fellow, 2014-present
University of Virginia, Charlottesville, Virginia USA
Ph.D., Mathematics, May 2014 – Advisor: Zoran Grujić
Virginia Commonwealth University, Richmond, Virginia USA
B.S., Pure Mathematics, May, 2009
B.S., Computer Science, May, 2009
Publications
1. Local analyticity radii of solutions to the 3D Navier-Stokes equations with locally
analytic forcing, (with Z. Grujić and I. Kukavica), to appear in J. Diff. Eq.
2. A spatially localized L log L estimate on the vorticity in the 3D NSE (with Z.
Grujić), to appear in I. Univ. Math. J.
3. A note on the temperature variance cascade in surface quasi-geostrophic turbulence (with Z. Grujić). to appear in Comm. Math. Sci.
4. Blow-up scenarios for 3D NSE exhibiting sub-criticality with respect to the scaling of one-dimensional local sparseness (with Zoran Grujić), J. Math. Fluid
Mech. (2013)
5. Energy cascades in physical scales of 3D incompressible magnetohydrodynamic
turbulence (with Zoran Grujić), J. Math. Phys. 54, (2013)
6. On the transport and concentration of enstrophy in 3D magnetohydrodynamic
turbulence (with Zoran Grujić), Nonlinearity 26 (2013), p. 2373
7. Geometric measure-type regularity criteria for the 3D magnetohydrodynamical
system, Nonlinear Analysis 75 (2012), p. 6180
8. Minimum cycle bases of direct products of graphs with cycles (with R. Hammack), Ars Mathematica Contemporanea 2 (2009), p. 101
9. Minimum cycle bases for direct products of K2 with complete graphs (with
M.M.M. Jaradat), Australasian Journal of Combinatorics 43 (2009), p. 127
Submitted &
Current Work
1. Scaling vs. dynamics in the 3D NSE. A vignette, (with Z .Grujić) (submitted)
Expository Work 1. Analyticity radii and the Navier-Stokes Equations: recent results and applications, (with Z. Grujić and I. Kukavica)
Awards &
Fellowships
SIAM Student Travel Award for the SIAM Conference on Analysis of Partial Differential Equations, Dec 2013.
Virginia Space Grant Consortium Graduate STEM Research Fellowship, 2012-2014.
Virginia Commonwealth University Outstanding Graduate in Pure Mathematics,
May, 2009.
Virginia Commonwealth University Provost Award Scholarship, 2005-2009.
Presentations
• Analytical properties for 3D NSE and applications, Univ. Illinois at Chicago
Applied Math. Seminar (Feb. 2015)
• Dynamics versus scaling in 3D NSE, UBC Diff. Geom, Math. Phys., PDE Seminar (Oct. 2014)
• Surface quasi-geostrophic turbulence, Virginia Space Grant Consortium Student
Research Conference, Norfolk, VA (April 2014)
• Local analytical properties of solutions to 3D NSE, 2014 AMS Spring Sectional
(April 2014)
• The 3D Navier-Stokes equations, vortex stretching, and logarithmic subcriticality, 2014 Joint Mathematics Meeting – AMS Special Session on Regulatory Problems for Nonlinear PDEs Modeling Fluids and Complex Fluids, Baltimore, MD
(Jan. 2014)
• Temperature variance cascades in surface quasi-geostrophic turbulence, 2013 SIAM
Conference on Analysis of Partial Differential Equations, Orlando, FL (Dec.
2013)
• On the transport and concentration of enstrophy in 3D MHD turbulence, Summer
School and Workshop: “Recent Advances in PDEs and Fluids,” Stanford, CA
(Aug. 2013)
• Sub-critical blow-up scenarios for the 3D Navier-Stokes Equations, University of
Virginia Analysis Seminar, Charlottesville, VA (April 2013)
• A rigorous study of magnetohydrodynamical turbulence, Virginia Space Grant
Consortium Student Research Conference, Norfolk, VA (April 2013)
• Turbulent cascades in physical scales of 3D incompressible plasmas, International
winter school on mathematical fluid dynamics, Levico-Terme, It. (Dec. 2012)
• Mathematical results in plasma turbulence, University of Virginia Differential
Equations Seminar, Charlottesville, VA (Nov. 2012)
• A geometric measure criteria for the 3D magnetohydrodynamical system, The
Southeastern-Atlantic Regional Conference on Differential Equations at Wake
Forest University, Winston-Salem, NC (Oct. 2012)
• Harmonic measure and a PDE application, Virginia Commonwealth University
Analysis Seminar, Richmond, VA (Oct. 2012)
Professional
Activity
• Co-organizer: Special Session on Mathematical Fluid Dynamics and Turbulence,
AMS Spring Eastern Sectional Meeting Georgetown University, Washington,
DC.
Workshops &
Conferences
• IPAM Mathematics of Turbulence – Workshop I (UCLA, Oct. 2014)
• Summer School and Workshop: “Recent Advances in PDEs and Fluids” (Stanford University, CA, Aug. 2013)
• AMS Mathematical Research Communities – 2013 – Regularity Problems for
Nonlinear Partial Differential Equations Modeling Fluids and Complex Fluids
(Snowbird, UT, June 2013)
• Virginia Space Grant Consortium Student Research Conference (Norfolk, VA,
April 2013)
• International Winter School on Mathematical Fluid Dynamics (Levico-Terme,
It., Dec. 2012)
• The Southeastern-Atlantic Regional Conference on Differential Equations at
Wake Forest University (Winston-Salem, NC, Oct. 2012)
• Modeling and Control of Nonlinear Evolution Equations (SISSA, It., July 2011)
Teaching
Experience
• Instructor: Introduction to Linear Programming (University of British Columbia
– 2015)
• Instructor: Differential Calculus with Applications to Commerce and Social Sciences, (University of British Columbia – 2014)
• Instructor: Applied Calculus I, 3 semesters (University of Virginia – 2010-2012)
• Instructor: Applied Calculus II, 1 semester (University of Virginia – 2012)
• Instructor: Calculus I for Math and Science Majors, 2 semesters (University of
Virginia – 2012-2013)
• Teaching assistant: Calculus II for Math and Science Majors, 2 sections (University of Virginia – 2009)
• Teaching assistant: Transition to Higher Mathematics, 1 section (University of
Virginia – 2010)