Optimal decay rates for solutions to the incompressible Oldroyd-B model in R 3

Matthias Georg Hieber, Huanyao Wen, Ruizhao Zi

Research output: Contribution to journalArticle

Abstract

Consider the Cauchy problem for the incompressible Oldroyd-B model in R 3 . For the case a = 0, global existence results for weak solutions were derived by Lions and Masmoudi (2000 Chin. Ann. Math. B 21 13146), allowing the initial data to be arbitrarily large, whereas it is not known whether this assertion is also true for a -= 0. In this article, time decay estimates for weak solutions subject to arbitrary large data are given for the case a = 0. Furthermore, timedecay estimates are also given for strong solutions for a = 0, however, for small initial data. The decay estimates obtained are of the form that the kth order derivatives in L 2 decay as (1 + t)?34 ?k2 for k = 0, 1, 2 as t → ∞. Note that the coupling constant ω does not need to be small throughout this paper.

Original languageEnglish
Pages (from-to)833-852
Number of pages20
JournalNonlinearity
Volume32
Issue number3
DOIs
Publication statusPublished - 2019 Jan 29
Externally publishedYes

Fingerprint

Decay Estimates
Decay Rate
decay rates
Weak Solution
Large Data
decay
estimates
Strong Solution
Assertion
Global Existence
Existence Results
Cauchy Problem
Cauchy problem
Decay
chin
Derivative
Arbitrary
Model
Estimate
Derivatives

Keywords

  • Oldroyd-B equation
  • optimal decay rates
  • weak solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Optimal decay rates for solutions to the incompressible Oldroyd-B model in R 3 . / Hieber, Matthias Georg; Wen, Huanyao; Zi, Ruizhao.

In: Nonlinearity, Vol. 32, No. 3, 29.01.2019, p. 833-852.

Research output: Contribution to journalArticle

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