Work

Strong time regularity and decay of $${\textbf{L}}^\infty $$ solutions to $$2\times 2$$ systems of conservation laws

Year: 2026

Type: article

Abstract: We consider $$\textbf{L}^\infty $$ L ∞ solutions to $$2\times 2$$ 2 × 2 systems of conservation laws. For genuinely nonlinear systems we prove that finite entropy solutions (in particular entropy solutions, if a uniformly convex entropy exists) belong to $$C^0(\mathbb {R}^+,; \textbf{L}^1_{loc}(\mathbb {R}))$$ C 0 ( R + , ; L loc 1 ( R ) ) . Our second result establishes a dispersive-type decay estimate for vanishing viscosity solutions. Both results are unified by the use of a kinetic formulation.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03333-1

Author: Luca Talamini

Institution: 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: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni