On entropy conservation for general systems of conservation laws

Dębiec, Tomasz

doi:10.48550/arxiv.1910.05793

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Notation and Preliminaries2

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2020

2021

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Cited by 2 publications

(2 citation statements)

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“…We refer the reader to [7,25,38] for similar commutator estimates in the context of Onsager's conjecture on the energy/entropy equality for various systems.…”

Section: Notation and Preliminariesmentioning

confidence: 98%

On the uniqueness of solutions to hyperbolic systems of conservation laws

Ghoshal

Jana

Koumatos

2021

Journal of Differential Equations

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“…We refer the reader to [7,25,38] for similar commutator estimates in the context of Onsager's conjecture on the energy/entropy equality for various systems.…”

Section: Notation and Preliminariesmentioning

confidence: 98%

On the uniqueness of solutions to hyperbolic systems of conservation laws

Ghoshal

Jana

Koumatos

2021

Journal of Differential Equations

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“…We refer the reader to [7,24,37] for similar commutator estimates in the context of Onsager's conjecture on the energy/entropy equality for various systems.…”

Section: Notation and Preliminariesmentioning

confidence: 98%

On the uniqueness of solutions to hyperbolic systems of conservation laws

Ghoshal¹,

Jana²,

Koumatos³

2020

Preprint

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For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space B α,∞ q and satisfying a one-sided bound condition are unique within the class of dissipative solutions. The exponent α > 1/2 is universal independently of the nature of the nonlinearity and the Besov regularity need only be imposed in space when the system is expressed in appropriate variables. The proof utilises a commutator estimate which allows for an extension of the relative entropy method to the required regularity setting. The systems of elasticity, shallow water magnetohydrodynamics, and isentropic Euler are investigated, recovering recent results for the latter. Moreover, the article explores a triangular system motivated by studies in chromatography and constructs an explicit solution which fails to be Lipschitz, yet satisfies the conditions of the presented uniqueness result.

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On entropy conservation for general systems of conservation laws

Cited by 2 publications

References 21 publications

On the uniqueness of solutions to hyperbolic systems of conservation laws

On the uniqueness of solutions to hyperbolic systems of conservation laws

On the uniqueness of solutions to hyperbolic systems of conservation laws

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