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

Yuanyuan Dan, Feng Li, Haitao Ma and Yajuan Zhao ()
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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

Mathematics, 2025, vol. 13, issue 16, 1-22

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.

Keywords: compressible Oldroyd-B model; global well-posedness; decay rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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