Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System

26 Pages Posted: 26 Sep 2022

See all articles by Timothée Crin-Barat

Timothée Crin-Barat

University of Deusto

LING-YUN SHOU

Nanjing University of Aeronautics and Astronautics

Abstract

In this paper we study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove the global well-posedness of strong solutions satisfying the uniform estimates with respect to the relaxation parameter. Then, we justify the strong relaxation limit and exhibit an explicit convergence rate of the process. Our proof is based on an adaptation of the techniques developed in [10, 11] to be able to deal with the additional low-order nonlinear term.

Keywords: Jin-Xin approximation, relaxation limit, global well-posedness, Besov, Viscous conservation laws

Suggested Citation

Crin-Barat, Timothée and SHOU, LING-YUN, Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System. Available at SSRN: https://ssrn.com/abstract=4230185

Timothée Crin-Barat (Contact Author)

University of Deusto ( email )

Bilbao, 48007
Spain

LING-YUN SHOU

Nanjing University of Aeronautics and Astronautics ( email )

Yudao Street
210016
Nanjing,, 210016
China

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