Publications
Clink on the pictures for links to the journal version of the publication or, for preprints, the arXiv version. The publications are listed roughly in reverse chronological order.
Abbrescia, L. and Speck J., Advances in the theory of multi-dimensional shock waves for the compressible Euler equations, preprint, (2024), 13 pages
Fournodavlos G., Rodnianski, I., and Speck J., Stable Big Bang formation for Einstein’s equations: The complete sub-critical regime, Journal of the American Mathematical Society, 17, no. 3, (2023), 827-916
Disconzi, M., Luo, C., Mazzone, G., and Speck, J., Rough sound waves in 3D compressible Euler flow with vorticity, Selecta Mathematica, 28, no. 5, (2022), 1-153
Abbrescia, L. and Speck J., Remarkable localized integral identities for 3D compressible Euler flow and the double-null framework, (2020), 83 pages
Speck, J., Multidimensional nonlinear geometric optics for transport operators with applications to stable shock formation, Pure and Applied Analysis, 1, no. 3, (2019), 447-514
Speck, J., The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology S^3, Communications in Mathematical Physics, 364, no. 3, (2018), 879-979
Rodnianski, I. and Speck, J., A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation, Annals of Mathematics, 187, no. 1, (2018), 65-156
Speck, J., A summary of some new results on the formation of shocks in the presence of vorticity, in Nonlinear Analysis in Geometry and Applied Mathematics; Harvard University Center of Mathematical Sciences and Applications, 1, (2017), 133-157
Holzegel, G., Klainerman, S., Speck, J., and Wong W., Shock formation in small-data solutions to 3D quasilinear wave equations: An overview, Journal of Hyperbolic Differential Equations, 13, no. 1, (2016), 1-105
Speck, J., The stabilizing effect of spacetime expansion on relativistic fluids with sharp results for the radiation equation of state, Archive for Rational Mechanics and Analysis, 210, no. 2, (2013), 535-579
Speck, J., The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system, Journal of Mathematical Physics, 53, no. 8, (2012), 1-83
Speck, J., Well-posedness for the Euler-Nordström system with cosmological constant, Journal of Hyperbolic Differential Equations, 6, no. 2, (2009), 313-358
Abbrescia, L. and Speck J., Lecture notes on: The emergence of the singular boundary from the crease in 3D compressible Euler flow, (2023), 294 pages
Abbrescia, L. and Speck J., The emergence of the singular boundary from the crease in 3D compressible Euler flow, (2022), 266 pages
Rodnianski, I. and Speck, J., On the nature of Hawking's incompleteness for the Einstein-vacuum equations: The regime of moderately spatially anisotropic initial data, Journal of the European Mathematical Society, 24, no. 1, (2022), 167-263
Speck, J., Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities, Analysis & PDE, 13, no. 1, (2020), 93-146
Disconzi, M. and Speck, J., The relativistic Euler equations: Remarkable null structures and regularity properties, Annales Henri Poincaré, 20, no. 7, (2019), 2173-2270
Luk, J. and Speck, J., Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity, Inventiones Mathematicae, 214, no. 1, (2018), 1-169
Speck, J., Shock formation for 2D quasilinear wave systems featuring multiple speeds: Blowup for the fastest wave, with non-trivial interactions up to the singularity, Annals of PDE, 4, no. 1, (2018), 1-131
Speck, J., Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations, Analysis & PDE, 10, no. 8, (2017), 2001-2030
Hadžić, M. and Speck, J., The global future stability of the FLRW solutions to the dust-Einstein system with a positive cosmological constant, Journal of Hyperbolic Differential Equations, 12, no. 1, (2015), 87-188
Rodnianski, I. and Speck, J., The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant, Journal of the European Mathematical Society, 15, no. 6, (2013), 2369-2462
Speck, J. and Strain, R., Hilbert expansion from the Boltzmann equation to relativistic fluids, Communications in Mathematical Physics, 304, no. 1, (2011), 229-280
Abbrescia, L. and Speck J., The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions, Classical and Quantum Gravity, 40, (2023), 1-80
Luk, J. and Speck J., The stability of simple plane-symmetric shock formation for 3D compressible Euler flow with vorticity and entropy, Analysis & PDE, 17, no. 3, (2024), 831-941
Luk, J. and Speck, J., The hidden null structure of the compressible Euler equations and a prelude to applications, Journal of Hyperbolic Differential Equations, 17, no. 1, (2020), 1-60
Speck, J., A new formulation of the 3D compressible Euler equations with dynamic entropy: Remarkable null structures and regularity properties, Archive for Rational Mechanics and Analysis, 234, no. 3, (2019), 1223-1279
Hadžić, M., Shkoller, S., and Speck, J., A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary, Communications in Partial Differential Equations, 44, no. 10, (2019), 859-906
Rodnianski, I. and Speck, J., Stable Big Bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems, Selecta Mathematica, 24, no. 5, (2018), 4293-4459
Speck, J., Holzegel, G., Luk, J., and Wong, W., Stable shock formation for nearly simple outgoing plane symmetric waves, Annals of PDE, 2, no. 2 (2016), 1-198
Speck, J., Shock formation in small-data solutions to 3D quasilinear wave equations, AMS Mathematical Surveys and Monographs, Vol. 214, (2016), 515 pages
Speck, J., The global stability of the Minkowski spacetime solution to the Einstein-nonlinear system in wave coordinates, Analysis & PDE, 7, no. 4, (2014), 771-901
Speck, J., The nonlinear future stability of the FLRW family of solutions to the Euler-Einstein system with a positive cosmological constant, Selecta Mathematica, 18, no. 3, (2012), 633-715
Speck, J., The non-relativistic limit of the Euler-Nordström system with cosmological constant, Reviews in Mathematical Physics, 21, no. 7, (2009), 821-876