@inproceedings{9ce7b9aea8794585b20fe005c8ba9479,
title = "Partial Regularity in Time for the Landau Equation (with Coulomb Interaction)",
abstract = "The present paper gives a simplified presentation of a partial regularity result obtained in a joint work with M. P. Gualdani, C. Imbert and A. Vasseur [arXiv:1906.02841 [math.AP]] for the spatially homogeneous Landau equation with Coulomb interaction in three space dimensions. Specifically, we prove that the procedure used in [C. Villani: Arch. Rational Mech. Anal. 143 (1998), 273–307] to construct H-solutions of the Landau equation leads to a class of weak solutions satisfying a truncated relative entropy estimate for values of the distribution function larger than any arbitrary level κ> 0. Using the method introduced in [E. De Giorgi: Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat., 3 (1957), 25–43] for studying the regularity of parabolic equations with bounded diffusion coefficients, we prove that the set of singular times of any such solution has Hausdorff dimension at most 1/2.",
keywords = "DeGiorgi-Nash-Moser regularity theory, Hausdorff dimension, Landau equation, Partial regularity",
author = "Fran{\c c}ois Golse",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; International Conference on Particle Systems and PDEs VI, VII and VIII, 2017-2019 ; Conference date: 02-12-2019 Through 06-12-2019",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-69784-6\_13",
language = "English",
isbn = "9783030697839",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "283--300",
editor = "C{\'e}dric Bernardin and Fran{\c c}ois Golse and Patr{\'i}cia Gon{\c c}alves and Valeria Ricci and Soares, \{Ana Jacinta\}",
booktitle = "From Particle Systems to Partial Differential Equations - International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019",
}