Communications in Mathematical Sciences

Volume 21 (2023)

Number 5

A class of global large solutions to the Oldroyd-B-type model with fractional dissipation

Pages: 1349 – 1362



Yichen Dai (School of Science, Jimei University, Xiamen, Fujian, China)

Zhong Tan (School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China; and Shenzhen Research Institute of Xiamen University, Shenzhen, China)

Jiahong Wu (Department of Mathematics, Oklahoma State University, Stillwater, Ok., U.S.A.)


The global existence and regularity problem on the Oldroyd‑B‑type model with fractional dissipation is not well understood for many ranges of fractional powers. This paper examines this open problem from a different perspective. We construct a class of large solutions to the $d$‑dimensional $(d=2,3)$ Oldroyd‑B‑type models with the fractional dissipation $(-\Delta)^\alpha u$ and $(-\Delta)^\beta \tau$ when the fractional powers satisfy $\alpha + \beta \geq 1$. The process presented here actually assesses that an initial data near any function whose Fourier transform lives in a compact set away from the origin always leads to a unique and global solution.


large solutions, Oldroyd-B-type model, fractional dissipation

2010 Mathematics Subject Classification

35Axx, 35Q35, 76D03

Received 31 October 2021

Accepted 18 October 2022

Published 30 August 2023