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Article

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

by
Yuanyuan Dan
1,
Feng Li
2,
Haitao Ma
3 and
Yajuan Zhao
4,*
1
School of Statistics and Data Science, Guangdong University of Finance and Economics, Guangzhou 510320, China
2
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
3
College of Mathematics Science, Harbin Engineering University, Harbin 150001, China
4
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(16), 2589; https://doi.org/10.3390/math13162589
Submission received: 30 June 2025 / Revised: 6 August 2025 / Accepted: 8 August 2025 / Published: 13 August 2025
(This article belongs to the Section C: Mathematical Analysis)
Versions Notes

Abstract

In this paper, we are concerned with the Cauchy problem of the compressible Oldroyd-B model without stress diffusion in Rn(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 Lp 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.
Keywords: compressible Oldroyd-B model; global well-posedness; decay rates compressible Oldroyd-B model; global well-posedness; decay rates

Share and Cite

MDPI and ACS Style

Dan, Y.; Li, F.; Ma, H.; Zhao, Y. On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion. Mathematics 2025, 13, 2589. https://doi.org/10.3390/math13162589

AMA Style

Dan Y, Li F, Ma H, Zhao Y. On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion. Mathematics. 2025; 13(16):2589. https://doi.org/10.3390/math13162589

Chicago/Turabian Style

Dan, Yuanyuan, Feng Li, Haitao Ma, and Yajuan Zhao. 2025. "On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion" Mathematics 13, no. 16: 2589. https://doi.org/10.3390/math13162589

APA Style

Dan, Y., Li, F., Ma, H., & Zhao, Y. (2025). On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion. Mathematics, 13(16), 2589. https://doi.org/10.3390/math13162589

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