A blow-down mechanism for the Landau-Coulomb equation

Gualdani, Maria Pia and Winter, Raphael 2025. A blow-down mechanism for the Landau-Coulomb equation. Journal of Functional Analysis 288 (7) , 110816. 10.1016/j.jfa.2024.110816

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Abstract

We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian function. We establish global well-posedness and show that the initial bump region will disappear in a time of order one. We prove that the function remains close to an explicit function during the blow-down. As a consequence, our result shows stretched exponential decay in time of the solution towards equilibrium. The key ingredients of our proof are the explicit blow-down function and a novel two-scale linearization in appropriate time-dependent spaces that yields uniform estimates in the perturbation parameter.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0022-1236
Date of First Compliant Deposit:	22 January 2025
Date of Acceptance:	31 December 2024
Last Modified:	29 Jan 2025 14:15
URI:	https://orca.cardiff.ac.uk/id/eprint/175519

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