Work

Liouville type theorem and kinetic formulation for 2×2 systems of conservation laws

Year: 2026

Type: article

Abstract: We study L∞ entropy solutions to 2×2 systems of conservation laws. We show that, if a uniformly convex entropy exists, these solutions satisfy a pair of kinetic equations (nonlocal in velocity), which are then shown to characterize all solutions with finite entropy production. Next, we prove a Liouville-type theorem for genuinely nonlinear systems, which is the main result of the paper. This implies in particular that for every finite entropy solution, every point (t,x)∈R+×R∖J is of vanishing mean oscillation, where J⊂R+×R is a set of Hausdorff dimension at most 1.

Source: Communications in Partial Differential Equations

DOI: 10.1080/03605302.2026.2735909

Authors: Fabio Ancona, Elio Marconi, Luca Talamini

Institutions: University of Padua, Scuola Internazionale Superiore di Studi Avanzati

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Horizon 2020 Framework Programme

Awards: G3345895242, G5245466801, G5796505130