Research interests: Analysis of Partial Differential Equations, Fluid Mechanics

Supervisor: Professor Edriss S. Titi

Email address: dwb42@cam.ac.uk

Education and Career

Since 2021: PhD in the Mathematics of Information, University of Cambridge

2020-2021: MASt, Part III Mathematics, University of Cambridge

2017-2020: Double Bachelor's degree in Mathematics and Physics, University of Groningen

Publications

• D.W. Boutros, E.S. Titi: On the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations. arXiv:2410.00813
• D.W. Boutros, S. Markfelder, E.S. Titi: Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations. Journal of Nonlinear Science 34, 68 (2024): arXiv:2305.14505
• C. Bardos, D.W. Boutros, E.S. Titi: Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains. arXiv:2304.01952
• D.W. Boutros, J.D. Gibbon: Phase transitions in the fractional three-dimensional Navier-Stokes equations. Nonlinearity 37, 4 (2024). arXiv:2303.07780
• D.W. Boutros, S. Markfelder, E.S. Titi: On Energy Conservation for the Hydrostatic Euler Equations: An Onsager Conjecture. Calculus of Variations and Partial Differential Equations 62, 219 (2023): arXiv:2208.08334
• D.W. Boutros, E.S. Titi: Onsager's Conjecture for Subgrid Scale α-Models of Turbulence. Physica D: Nonlinear Phenomena 443, 1–23 (2023): arXiv:2207.03416

Other Works

• D.W. Boutros: On Energy Conservation for the Hydrostatic Euler Equations: An Onsager Conjecture. Oberwolfach Report 51 (2022), pp. 23-25

Talks

• June 2024: Fractional Calculus Seminar Series, SISSA, International School of Advanced Studies (recording)
• March 2024: Nonlinear PDE and Mathematical Physics Seminar, Texas A&M University
• February 2024: Anti-diffusive dynamics programme seminar, Isaac Newton Institute Cambridge (recording, slides)
• February 2024: Oberseminar Mathematical Fluid Dynamics, University of Würzburg
• January 2024: Turbulence on the Banks of the Arno, Scuola Normale Superiore Pisa
• January 2024: Zürich Graduate Colloquium in Applied Mathematics, ETH Zürich
• December 2023: Online seminar for DFG Research Unit on Geophysical Flows
• December 2023: Oberseminar Mathematical Fluid Dynamics, University of Würzburg
• November 2023: Kick-off meeting of DFG Research Unit on Geophysical Flows, TU Darmstadt
• November 2023: Scaling Cascades in Complex Systems Days, Berlin
• October 2023: Recent Topics on the Navier-Stokes Equations, Oberwolfach
• December 2022: Junior Analysis Seminar, Imperial College London
• November 2022: CCIMI Conference, Isaac Newton Institute Cambridge (recording, slides)
• November 2022: Mathematical Advances in Geophysical Fluid Dynamics, Oberwolfach
• November 2022: Graduate seminar on Advanced topics in PDE, University of Bonn
• October 2022: Wolfson College Science Society
• July 2022: 2nd IST Austria Summer School in Analysis and PDEs, IST Austria
• June 2022: Junior Isaac Newton Crossover seminar, Isaac Newton Institute Cambridge (recording, slides)
• May 2022: Uncertainty Quantification : Recent Advances in the Mathematics of Information, Møller Institute, Churchill College, Cambridge (recording)
• May 2022: Nonlinear PDEs in Fluid Mechanics, CIRM Marseille Luminy (slides)

Poster Presentations

• January 2024: Layering — A structure formation mechanism in oceans, atmospheres, active fluids and plasmas, Isaac Newton Institute Cambridge
• August 2022: Hausdorff School on Geometric Analysis and Nonlinear Partial Differential Equations, University of Bonn
• July 2022: When Kinetic Theory meets Fluid Mechanics, ETH Zürich
• May 2022: Advances in geophysical and astrophysical turbulence, Isaac Newton Institute Cambridge
• April 2022: Wolfson College Research Event

Teaching

• Michaelmas 2024: Example classes for Mathematical Analysis of the Incompressible Navier-Stokes Equations
• Michaelmas 2022: Supervisions for Part IB Linear Algebra and Drop-in Sessions for Analysis of Partial Differential Equations
• Easter 2022: Supervisions for Part II Analysis of Functions and Part IB Analysis and Topology
• Lent 2022: Supervisions for Part II Analysis of Functions
• Michaelmas 2021: Drop-in Sessions for Analysis of Partial Differential Equations and Distribution Theory and Applications