Research interests: 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 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 the conservation of helicity by weak solutions of the 3D Euler and
inviscid MHD equations

(2024)

Nonuniqueness of Generalised Weak Solutions to the Primitive and Prandtl Equations

– Journal of Nonlinear Science

(2024)

34,

68

(doi: 10.1007/s00332-024-10032-8)

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

– Nonlinearity

(2024)

37,

045010

(doi: 10.1088/1361-6544/ad25be)

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)