Well-posedness of the Lenard–Balescu equation with smooth Iinteractions

Duerinckx, Mitia and Winter, Raphael 2023. Well-posedness of the Lenard–Balescu equation with smooth Iinteractions. Archive for Rational Mechanics and Analysis 247 , 71. 10.1007/s00205-023-01901-9

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Abstract

The Lenard–Balescu equation was formally derived in the 1960s as the fundamental description of the collisional process in a spatially homogeneous system of interacting particles. It can be viewed as correcting the standard Landau equation by taking into account collective screening effects. Due to the reputed complexity of the Lenard–Balescu equation in case of Coulomb interactions, its mathematical theory has remained void apart from the linearized setting (Merchant and Liboff in J Math Phys 14(1):119-129, 1973; Strain in Commun Partial Differ Equ 32(10-12):1551-1586, 2007). In this contribution, we focus on the case of smooth interactions and we show that dynamical screening effects can then be handled perturbatively. Taking inspiration from the Landau theory, we establish global well-posedness close to equilibrium, local well-posedness away from equilibrium, and we discuss the convergence to equilibrium and the validity of the Landau approximation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0003-9527
Date of First Compliant Deposit:	19 March 2024
Date of Acceptance:	29 June 2023
Last Modified:	09 Nov 2024 14:30
URI:	https://orca.cardiff.ac.uk/id/eprint/167345

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