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

    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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