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Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism

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Abstract

We are concerned with the global well-posedness to the compressible Oldroyd-B model without a damping term in the stress tensor equation. By exploiting the intrinsic structure of the equations and introducing several new quantities for the density, the velocity and the divergence of the stress tensor, we overcome the difficulty of the lack of dissipation for the density and the stress tensor, and construct unique global solutions to this system with initial data in critical Besov spaces. As a byproduct, we obtain the optimal time decay rates of the solutions by using the pure energy argument. A similar result can be also proved for the compressible viscoelastic system without “div–curl" structure.

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Acknowledgements

This work is supported by the Guangdong Provincial Natural Science Foundation under the grant number 2022A1515011977 and the Science and Technology Program of Shenzhen under the grant number 20200806104726001.

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Authors and Affiliations

  1. Department of Mathematics, Guangdong University of Technology, Guangzhou, 510520, China

    Xiaoping Zhai

  2. School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Zhi-Min Chen

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  1. Xiaoping Zhai
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Correspondence to Xiaoping Zhai.

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Zhai, X., Chen, ZM. Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-023-10346-3

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  • DOI: https://doi.org/10.1007/s10884-023-10346-3

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