PTIMAL TIME-DECAY FOR EULER-FOURIER SYSTEM WITH DAMPING IN THE CRITICAL <i>L</i><sup>2</sup> FRAMEWORK

Jing Liu; Lianchao Gu

doi:10.11948/20250151

2026 Volume 16 Issue 2

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Jing Liu, Lianchao Gu. PTIMAL TIME-DECAY FOR EULER-FOURIER SYSTEM WITH DAMPING IN THE CRITICAL L2 FRAMEWORK[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 555-578. doi: 10.11948/20250151

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Jing Liu, Lianchao Gu. PTIMAL TIME-DECAY FOR EULER-FOURIER SYSTEM WITH DAMPING IN THE CRITICAL L² FRAMEWORK[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 555-578. doi: 10.11948/20250151

PTIMAL TIME-DECAY FOR EULER-FOURIER SYSTEM WITH DAMPING IN THE CRITICAL L² FRAMEWORK

Jing Liu^1,,
Lianchao Gu^1, ,

1.
School of Mathematics and Key Laboratory of Mathematical MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Author Bio: Email: liujing_18@nuaa.edu.cn(J. Liu)
Corresponding author: Email: gulianchao@nuaa.edu.cn(L. Gu)

Abstract

Abstract

This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in $ \mathbb{R}^{d}\; (d\geq1) $. In this study, a time-weighted energy argument has been developed within the $ L^{2} $ framework to derive the optimal time-decay rates. A great part of our analysis relies on the study of a Lyapunov functional in the spirit of [18], which mainly depends on some elaborate use of non-classical Besov product estimates and interpolations. Furthermore, exhibiting a damped mode with faster time decay than the whole solution also plays a key role.
- Euler-Fourier system with damping /
- critical regularity /
- optimal time-decay rate
MSC: 35Q31, 76N15

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References

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