Research interests: Partial differential equations, Fluid mechanics

Supervisor: Professor Edriss S. Titi

Email address: dwb42@cam.ac.uk

## Education

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, S. Markfelder, E.S. Titi:
*Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations*. 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*. 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 and Poster Presentations

- 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
- August 2022: Hausdorff School on Geometric Analysis and Nonlinear Partial Differential Equations, University of Bonn
- July 2022: 2nd IST Austria Summer School in Analysis and PDEs, IST Austria
- July 2022: When Kinetic Theory meets Fluid Mechanics, ETH Zürich
- 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: Advances in geophysical and astrophysical turbulence, Isaac Newton Institute Cambridge
- May 2022: Nonlinear PDEs in Fluid Mechanics, CIRM Marseille Luminy (slides)
- April 2022: Wolfson College Research Event

## Teaching

- 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

## Publications

On energy conservation for the hydrostatic Euler equations: an Onsager conjecture

– Calculus of Variations and Partial Differential Equations

(2023)

62,

219

(doi: 10.1007/s00526-023-02558-8)

Nonuniqueness of generalised weak solutions to the primitive and Prandtl
equations

(2023)

Hölder regularity of the pressure for weak solutions of the 3D Euler
equations in bounded domains

(2023)

Phase transitions in the fractional three-dimensional Navier-Stokes
equations

(2023)

Onsager's Conjecture for Subgrid Scale $α$-Models of Turbulence

– Physica D Nonlinear Phenomena

(2022)

443,

133553

(doi: 10.1016/j.physd.2022.133553)

On Energy Conservation for the Hydrostatic Euler Equations: An Onsager
Conjecture

(2022)