"When a continuous medium is deprived of its physical properties (elasticity, thermal and electrical conductivity, and so on) its property of occupying a definite position in space remains, as do elementary interactions through the mutual pressure of its parts, due to Aristotle’s principle that it is impossible for two bodies to occupy the same space. It is amazing that it is these elementary interactions that cause the most complicated effects, including turbulence." -- V. I. Yudovich

A summary of some of my research, written for the SCGP newsletter, is here. Here are lecture notes on turbulence theory, and here is a review paper on long time and singular behavior of fluid motion. Some of my work can be found on:

ORCID , Google Scholar, arXiv, MathSciNet, GitHub, Youtube.


Publications

63. T.D. Drivas and D. Glukhovskiy.
    Geometry of strong forces in continuum mechanics.
    submitted, (2026).


62. T.D. Drivas, B.A. Khanikati, and V.A. Khanikati.
    On the collapse of three point vortices on surfaces.
    submitted, (2026).


61. T.D. Drivas.
    Mathematical Theorems on Turbulence.
    submitted, (2025).


60. T.D. Drivas and M. Retakh.
    How doth the random triangle.
    submitted, (2025).


59. T.D. Drivas, D. Ginsberg and M. Nualart.
    On the fragility of laminar flow.
    submitted, (2025).


58. G.L. Eyink and T.D. Drivas.
    Quantum Spontaneous Stochasticity.
    preprint (2017).


57. L. De Rosa, T.D. Drivas, M. Inversi and P. Isett.
    Intermittency and dissipation regularity in turbulence.
    Archive for Rational Mechanics and Analysis, accepted (2026).


56. T.D. Drivas, L. Galeati, and U. Pappalettera.
    Anomalous Dissipation and Regularization in isotropic Gaussian turbulence.
    Annals of Probability, accepted (2026).


55. T.D. Drivas and M. Nualart.
    A geometric characterization of steady laminar flow.
    Communications on Pure and Applied Mathematics}, (2026).


54. T.D. Drivas, T.M. Elgindi, and D. Ginsberg.
    On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry.
    Pure and Applied Functional Analysis, accepted (2026).


53. T.D. Drivas and J. La.
    Lagrangian aspects of Yudovich theory for 2D Euler.
    Pure and Applied Functional Analysis, accepted (2026).


52. T.D. Drivas, D. Glukhovskiy, and B. Khesin.
    Pensive billiards, point vortices, and pucks.
    Forum of Mathematics, Sigma, (2025).


51. K. Iyer, T.D. Drivas, G. Eyink, and K. Sreenivasan.
    Turbulence without walls: Whither the zeroth law of turbulence?
    Physical Review Letters, Phys. Rev. Lett. 135, 134001, (2025).


50. T.D. Drivas, T. Elgindi, and I-J Jeong.
    Twisting in Hamiltonian Flows and Perfect Fluids.
    Inventiones mathematicae, 238, 331–370 (2024).


49. L. De Rosa, T.D. Drivas, and M. Inversi.
    On the support of anomalous dissipation measures.
    Journal of Mathematical Fluid Mechanics, 26, 56 (2024).


48. T.D. Drivas, D. Glukhovskiy, and B. Khesin.
    Singular vortex pairs follow magnetic geodesics.
    International Mathematics Research Notices, (14), 10880–10894 (2024).


47. T.D. Drivas, S. Iyer, and T.T. Nguyen.
    The Feynman–Lagerstrom criterion for boundary layers.
    Archive for Rational Mechanics and Analysis, 248, 55 (2024).


46. T.D. Drivas, and D. Ginsberg.
    Islands in stable fluid equilibria.
    Proceedings of the American Mathematical Society, 152, 4855--4863 (2024).


45. M. Coti Zelati, T.D. Drivas, and R. Gvalani.
    Statistically self-similar mixing by Gaussian random fields.
    Journal of Statistical Physics, 191, 61 (2024).


44. T. Buckmaster, T.D. Drivas, S. Shkoller, and V. Vicol.
    Formation and development of singularities for the compressible Euler equations.
    Proc. Int. Cong. Math. 2022, Vol. 5, pp. 3636–3659. EMS Press, Berlin, (2023).


43. S. Ananda, M. Bertagni, T.D. Drivas, and A. Porporato.
    Self-Similarity and Vanishing Diffusion Limit in Fluvial Landscapes.
    Proceedings of the National Academy of Sciences, (2023).


42. T.D. Drivas, A.A. Mailybaev, and A. Raibekas.
    Statistical determinism in non-Lipschitz dynamical systems.
    Ergodic Theory and Dynamical Systems, 1-29. (2023).


41. T.D. Drivas, D. Ginsberg, and H. Grayer II.
    On the distribution of heat in fibered magnetic fields.
    Communications in Mathematical Physics, 405, 57 (2024).


40. T.D. Drivas, A. Dunlap, C. Graham, J. La, and L. Ryzhik.
    Invariant measures for stochastic conservation laws on the line.
    Nonlinearity, 36 4553, (2023).


39. T.D. Drivas, T.M. Elgindi, and J. La.
    Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids.
    Mathematische Annalen, (2022).


38. M. Dolce and T.D. Drivas.
    On maximally mixed equilibria of two-dimensional perfect fluids.
    Archive for Rational Mechanics and Analysis, 246, 735–770 (2022).


37. T.D. Drivas and T.M. Elgindi.
    Singularity formation in the incompressible Euler equation in finite and infinite time.
    EMS Surveys in Mathematical Sciences}, 10, no. 1, pp. 1–100, (2023).


36. T. Buckmaster, T.D. Drivas, S. Shkoller, and V. Vicol.
    Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry.
    Annals of PDE, 8:26 (2022).


35. P. Constantin, T.D. Drivas, and D. Ginsberg.
    Flexibility and rigidity of free boundary MHD equilibria.
    Nonlinearity, 35 2363 (2022).


34. T.D. Drivas.
    Self–Regularization in turbulence from the Kolmogorov 4/5th Law and Alignment.
    Philosophical Transactions of the Royal Society A, 380: 20210033 (2022).


33. L. Bentkamp, T.D. Drivas, C.C. Lalescu, and M. Wilczek.
    The statistical geometry of material loops in turbulence.
    Nature Communications, 13, 2088 (2022).


32. T.D. Drivas, H.Q. Nguyen, and C. Nobili.
    Bounds on heat flux for Rayleigh-B\'enard convection between Navier-slip fixed-temperature boundaries.
    Philosophical Transactions of the Royal Society A, (2021).


31. T.D. Drivas, T.M. Elgindi, G. Iyer, and I--J. Jeong.
    Anomalous Dissipation in Passive Scalar Transport.
    Archive for Rational Mechanics and Analysis, 243, 1151-1180 (2022).


30. T.D. Drivas and J. La.
    Boundary conditions and polymeric drag reduction for the Navier-Stokes equations.
    Archive for Rational Mechanics and Analysis, 242(1), 485-526 (2021).


29. T.D. Drivas, G. Misiolek, B. Shi, and T. Yoneda.
    Conjugate and cut points in ideal fluid motion.
    Annales Mathematiques du Quebec, (2021).
    Special issue in honor of Professor Alexander Shnirelman's 75th birthday.


28. P. Constantin, T.D. Drivas, and D. Ginsberg.
    Flexibility and rigidity in steady fluid motion.
    Communications in Mathematical Physics, 385.1, 521-563 (2021).


27. P. Constantin, T.D. Drivas, and D. Ginsberg.
    On quasisymmetric plasma equilibria sustained by small force.
    Journal of Plasma Physics, 87.1 (2021).


26. D.C. Saunders, G. Frederick, T.D. Drivas, and S. Wunsch.
    Self-similar decay of the drag wake of a dimpled sphere.
    Physical Review Fluids, 5, 124607, (2020).


25. T.D. Drivas and A.A. Mailybaev.
    "Life after death" in ordinary differential equations with a non-Lipschitz singularity.
    Nonlinearity, 34 2296, (2021).


24. P. Constantin, T.D. Drivas and R. Shvydkoy.
    Entropy Hierarchies for equations of compressible fluids and self-organized dynamics.
    SIAM Journal Mathematical Analysis, 52 (3), 3073-3092 (2020).


23. P. Constantin, T.D. Drivas and T.M. Elgindi.
    {Inviscid limit of vorticity distributions in Yudovich class.
    Communications on Pure and Applied Mathematics, (2020).


22. M. Coti Zelati and. T.D. Drivas.
    {A stochastic approach to enhanced diffusion.
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (2020).


21. T.D. Drivas, D.D Holm, and J--M. Leahy.
    {Lagrangian averaged stochastic advection by Lie transport for fluids.
    Journal of Statistical Physics, 1-39 (2020).


20. T.D. Drivas and D.D. Holm.
    Energy and Circulation Theorem Preserving Stochastic Fluids.
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1-39, (2019).


19. T.D. Drivas and G.L. Eyink.
    An Onsager Singularity Theorem for Leray Solutions of the Navier-Stokes Equations.
    Nonlinearity, 32.11, 4465, (2019).


18. P. Constantin, T.D. Drivas, H.Q. Nguyen and F. Pasqualotto.
    Compressible Fluids and Active Potentials.
    Annales de l'Institut Henri Poincare C, Analyse Non Lineaire, (2019).


17. T.D. Drivas.
    Turbulent Cascade Direction and Lagrangian Time-Asymmetry.
    Journal of Nonlinear Science, 29: 65, (2019).


16. T.D. Drivas and H.Q. Nguyen.
    Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit.
    Journal of Nonlinear Science, 1-13, (2018).


15. T.D. Drivas and H.Q. Nguyen.
    Onsager's conjecture and anomalous dissipation on domains with boundary.
    SIAM Journal Mathematical Analysis, 50(5), 4785–4811 (2018).


14. T.D. Drivas and G.L. Eyink.
    An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations.
    Communications in Mathematical Physics, 359: 733, (2018).


13. G.L. Eyink and T.D. Drivas.
    Cascades and Dissipative Anomalies in Compressible Fluid Turbulence.
    Physical Review X, 8, 011022, (2018).


12. G.L. Eyink and T.D. Drivas.
    Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence.
    Physical Review X, 8, 011023, (2018).


11. T.D. Drivas, P.L. Johnson, C.C. Lalescu and M. Wilczek.
    On the large-scale sweeping of small-scale eddies in turbulence -- A filtering approach.
    Physical Review Fluids, 2, 104603, (2017).


10. G.L. Eyink and T.D. Drivas.
    A Lagrangian fluctuation-dissipation relation for scalar turbulence, III.
    Journal of Fluid Mechanics, 829, 153-189 (2017).


9. T.D. Drivas and G.L. Eyink.
   A Lagrangian fluctuation-dissipation relation for scalar turbulence, II.
   Journal of Fluid Mechanics, 829, 153-189 (2017).


8. T.D. Drivas and G.L. Eyink.
   A Lagrangian fluctuation-dissipation relation for scalar turbulence, I.
   Journal of Fluid Mechanics, 829, 153-189 (2017).


7. T.D. Drivas and S.E. Wunsch.
   Internal tide energy transfer by nonlinear refraction.
   VIIIth International Symposium on Stratified Flows}, Vol. 1. No. 1. (2016).


6. T.D. Drivas and S.E. Wunsch.
   Triad Resonance between Gravity and Vorticity Waves in Vertical Shear.
   Ocean Modelling, 103 87-97 (2016).


5. C.C. Lalescu, Y--K. Shi, G.L. Eyink, T.D. Drivas, E. Vishniac and A. Lazarian.
   Inertial-Range Reconnection in Magnetohydrodynamic Turbulence and in the Solar Wind.
   Physical Review Letters, 115, 025001 (2015).


4. G.L. Eyink and T.D. Drivas.
   Spontaneous Stochasticity and Anomalous Dissipation in Burgers Equation.
   Journal of Statistical Physics, 158, Issue 2, 386--432 (2014).


3. D. Benveniste and T.D. Drivas.
   Asymptotic results for backwards two-particle dispersion in a turbulent flow.
   Physical Review E, 89, 041003(R) (2014).


2. A.I. Harte and T.D. Drivas.
   Caustics and wave propagation in curved spacetimes.
   Physical Review D, 85, 124039 (2012).


1. T.D. Drivas and S.E. Gralla.
   Dependence of Self-Force on Central Object.
   Classical and Quantum Gravity, 28, 145025 (2011)

PhD Thesis

Anomalous Dissipation, Spontaneous Stochasticity & Onsager’s Conjecture


Current Support: Stony Brook University Trustee’s award, Alfred P. Sloan Fellowship, NSF CAREER award #2235395 and NSF #2106233
Past Support: NSF #1703997