Uniform bound of the highest-order energy for three dimensional inhomogeneous incompressible elastodynamics

Xiufang Cui; Xianpeng Hu; Xiufang Cui; Xianpeng Hu

doi:10.3934/cam.2025018

Communications in Analysis and Mechanics

2025, Volume 17, Issue 2: 429-461. doi: 10.3934/cam.2025018

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Uniform bound of the highest-order energy for three dimensional inhomogeneous incompressible elastodynamics

Xiufang Cui ¹,
Xianpeng Hu ^{2
,
,}

1.
School of Mathematics and Statistics, Lanzhou University, Gansu 730000, P.R.China
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, P.R.China

Received: 31 December 2024 Revised: 21 April 2025 Accepted: 23 April 2025 Published: 07 May 2025
35L72, 35Q74, 74B20

We are concerned with the time growth of the highest-order energy of three-dimensional inhomogeneous incompressible isotropic elastodynamics. Utilizing Klainerman's generalized energy method, refined weighted estimates, and the Keel-Smith-Sogge estimate [J. Anal. Math., 87: 265-279, 2002], it is justified that the highest-order generalized energy is uniformly bounded for all time.
- inhomogeneous incompressible elastodynamics,
- uniform bound,
- highest-order energy,
- KSS estimate,
- vector field theory
Citation: Xiufang Cui, Xianpeng Hu. Uniform bound of the highest-order energy for three dimensional inhomogeneous incompressible elastodynamics[J]. Communications in Analysis and Mechanics, 2025, 17(2): 429-461. doi: 10.3934/cam.2025018

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Abstract

We are concerned with the time growth of the highest-order energy of three-dimensional inhomogeneous incompressible isotropic elastodynamics. Utilizing Klainerman's generalized energy method, refined weighted estimates, and the Keel-Smith-Sogge estimate [J. Anal. Math., 87: 265-279, 2002], it is justified that the highest-order generalized energy is uniformly bounded for all time.

References

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