Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations
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- by Jacob Bedrossian, Maria Pia Gualdani and Stanley Snelson PDF
- Trans. Amer. Math. Soc. 375 (2022), 2187-2216 Request permission
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.References
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Additional Information
- Jacob Bedrossian
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 908903
- Email: jacob@cscamm.umd.edu
- Maria Pia Gualdani
- Affiliation: Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Austin, Texas 78712
- MR Author ID: 709090
- ORCID: 0000-0002-6830-1606
- Email: gualdani@math.utexas.edu
- Stanley Snelson
- Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901
- MR Author ID: 966432
- Email: ssnelson@fit.edu
- Received by editor(s): June 1, 2021
- Received by editor(s) in revised form: September 18, 2021
- Published electronically: December 23, 2021
- Additional Notes: The first author was partially supported by National Science Foundation RNMS #1107444 (Ki-Net). The second author was partially supported by the DMS-NSF 2019335 and would like to thanks NCTS Mathematical division Taipei for their kind hospitality. The third author was partially supported by a Ralph E. Powe Award from ORAU
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 2187-2216
- MSC (2020): Primary 35B44; Secondary 35Q83, 35Q20
- DOI: https://doi.org/10.1090/tran/8568
- MathSciNet review: 4378091