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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
DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n5.a8
Authors
Abstract
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.
Keywords
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