Global Small Solutions to a Complex Fluid Model in Three Dimensional

Fang-Hua Lin, Ting Zhang

Research output: Contribution to journalArticle

Abstract

In this paper, we provide a much simplified proof of the main result in Lin and Zhang (Commun Pure Appl Math 67: 531–580, 2014) concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a three dimensional incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Besides the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the L<sup>∞</sup> estimates for time slices to deduce the key L<sup>1</sup> in time estimates. The latter is responsible for the global in time existence.

Original languageEnglish (US)
Pages (from-to)905-920
Number of pages16
JournalArchive for Rational Mechanics and Analysis
Volume216
Issue number3
DOIs
StatePublished - Jun 1 2015

Fingerprint

Complex Fluids
Small Solutions
Fluid Model
Three-dimensional
Fluids
Incompressibility
Energy Estimates
Energy Method
Smooth Solution
Algebraic Structure
Equilibrium State
Slice
Incompressible Fluid
Estimate
Global Existence
Deduce
Cauchy Problem
Existence and Uniqueness
Fluid

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Global Small Solutions to a Complex Fluid Model in Three Dimensional. / Lin, Fang-Hua; Zhang, Ting.

In: Archive for Rational Mechanics and Analysis, Vol. 216, No. 3, 01.06.2015, p. 905-920.

Research output: Contribution to journalArticle

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