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Research

Grigalius Taujanskas

Trinity Hall, Cambridge, UK
FORTH, Crete, Greece

Research

Broadly, I am interested in partial differential equations arising in general relativity and mathematical physics. I am particularly interested in nonlinear wave equations, the regularity properties of hyperbolic and dispersive PDEs, scattering theory, and the geometry and physics of asymptotic structures of spacetimes and fields.

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Publications

Papers

  1. Controlled regularity at future null infinity from past asymptotic initial data: the wave equation (with J. Marajh and J. A. Valiente Kroon).
    Submitted (2025).
    arXiv:2508.04690, 30 pages.
  2. Global finite energy solutions of the Maxwell-scalar field system on the Einstein cylinder (with J.-P. Nicolas).
    Submitted (2025).
    arXiv:2507.16750, 46 pages.
  3. One-dimensional Carrollian fluids III: global existence and weak continuity in L∞ (with P. M. Petropoulos and S. Schulz).
    Journal of the London Mathematical Society 111 (6), e70186 (2025).
    arXiv:2407.05972, 31 pages.
  4. One-dimensional Carrollian fluids II: C1 blow-up criteria
    (with N. Athanasiou, P. M. Petropoulos, and S. Schulz).
    Journal of the London Mathematical Society 112 (5), e70354 (2025).
    arXiv:2407.05971, 24 pages.
  5. One-dimensional Carrollian fluids I: Carroll–Galilei duality
    (with N. Athanasiou, P. M. Petropoulos, and S. Schulz).
    Journal of High Energy Physics (JHEP) 11 (2024) 012.
    arXiv:2407.05962, 23 pages.
  6. Wave map null form estimates via Peter–Weyl theory.
    Journal of Functional Analysis 289 (6), 111040 (2025).
    arXiv:2307.13052, 36 pages.
  7. Controlled regularity at future null infinity from past asymptotic initial data: massless fields (with J. A. Valiente Kroon).
    Submitted (2023).
    arXiv:2304.08270, 42 pages.
  8. Conformal scattering of Maxwell potentials (with J.-P. Nicolas).
    Annales de l'Institut Fourier 76 (3), 1207–1274 (2026).
    arXiv:2211.14579, 48 pages.
  9. Large data decay of Yang–Mills–Higgs fields on Minkowski and de Sitter spacetimes.
    Journal of Mathematical Physics 60 (12), 121504 (2019).
    arXiv:1902.08519, 22 pages.
  10. Conformal scattering of the Maxwell-scalar field system on de Sitter space.
    Journal of Hyperbolic Differential Equations 16 (04), 743–791 (2019).
    arXiv:1809.01559, 39 pages.

Proceedings

  1. Intro: at the interface of asymptotics, conformal methods, and analysis in general relativity (with J. A. Valiente Kroon).
    Philosophical Transactions of the Royal Society A 382:20230048 (2024).
  2. Scattering of Maxwell potentials on curved spacetimes.
    Ghent Methusalem Colloquium: Extended Abstracts 21/22, pp. 57–64 (2024).
    arXiv:2307.08398, 6 pages.

Edited Volumes

  1. At the interface of asymptotics, conformal methods and analysis in general relativity (with J. A. Valiente Kroon).
    Philosophical Transactions of the Royal Society A 382 (2267) (2024).

    Proceedings for the conference of the same title, which took place at the Royal Society in London on 9–10 May 2023.

PhD Thesis