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arXiv · 2105.03942

Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations

Jacob Bedrossian·Maria Pia Gualdani·Stanley Snelson
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Abstract

We consider the homogeneous and inhomogeneous Landau equation for very soft and Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not exist under mild decay assumptions on the profile. We extend our analysis to the Vlasov-Poisson-Landau system and to the Boltzmann equation without angular cut-off.

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Jacob Bedrossian, Maria Pia Gualdani, Stanley Snelson. 2021-05-09. Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations. https://arxiv.org/abs/2105.03942

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