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On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion

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  • Yuanyuan Dan

    (School of Statistics and Data Science, Guangdong University of Finance and Economics, Guangzhou 510320, China)

  • Feng Li

    (School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China)

  • Haitao Ma

    (College of Mathematics Science, Harbin Engineering University, Harbin 150001, China)

  • Yajuan Zhao

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

Abstract

In this paper, we are concerned with the Cauchy problem of the compressible Oldroyd-B model without stress diffusion in R n ( n = 2 , 3 ) . The absence of stress diffusion introduces significant challenges in the analysis of this system. By employing tools from harmonic analysis, particularly the Littlewood–Paley decomposition theory, we establish the global well-posedness of solutions with initial data in L p critical spaces, which accommodates the case of large, highly oscillating initial velocity. Furthermore, we derive the optimal time decay rates of the solutions by a suitable energy argument.

Suggested Citation

  • Yuanyuan Dan & Feng Li & Haitao Ma & Yajuan Zhao, 2025. "On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion," Mathematics, MDPI, vol. 13(16), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2589-:d:1723445
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