Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 9
179
Views
2
CrossRef citations to date
0
Altmetric
Articles

Global regularity for d-dimensional micropolar equations with fractional dissipation

&
Pages 1567-1580 | Received 11 Aug 2017, Accepted 22 Jan 2018, Published online: 06 Feb 2018

References

  • Cowin SC . Polar fluids. Phys Fluids. 1968;11:1919–1927.
  • Erdogan ME . Polar effects in the apparent viscosity of suspension. Rheol Acta. 1970;9:434–438.
  • Eringen AC . Theory of micropolar fluids. J Math Mech. 1966;16:1–18.
  • Eringen AC . Micropolar fluids with stretch. Int J Eng Sci. 1969;7:115–127.
  • Lukaszewicz G . Micropolar fluids. Theory and applications. Modeling and simulation in science, engineering and technology. Boston: Birkhäuser; 1999.
  • Popel S , Regirer A , Usick P . A continuum model of blood flow. Biorheology. 1974;11:427–437.
  • Stokes VK . Theories of fluids with microstructure. New York (NY): Springer; 1984.
  • Chen M , Xu X , Zhang J . The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect. Z Angew Math Phys. 2014;65:687–710.
  • Chen Q , Miao C . Global well-posedness for the micropolar fluid system in critical Besov spaces. J Differ Equ. 2012;252:2698–2724.
  • Dong B , Chen Z . Regularity criteria of weak solutions to the three-dimensional micropolar flows. J Math Phys. 2009;50:103525.
  • Galdi G , Rionero S . A note on the existence and uniqueness of solutions of micropolar fluid equations. Int J Eng Sci. 1977;14:105–108.
  • Xu Z , Zhu X , Li H , et al . The control of the boundary layer for the micropolar fluid equations with zero limits of angular and microrotational viscosities. Z Angew Math Phys. 2017;68, Art. 60, 23 pp.
  • Yuan B . Regularity of weak solutions to magneto-micropolar fluid equations. Acta Math Sci. 2010;30B:1469–1480.
  • Zhu X , Xu Z , Li H . The boundary effects and zero angular and micro-rotational viscosities limits of the micropolar fluid equations. Acta Appl Math. 2017;147:113–136.
  • Constantin P , Foias C . Navier-Stokes equations. Chicago lectures in mathematics. Chicago (IL): University of Chicago Press; 1989.
  • Doering C , Gibbon J . Applied analysis of the Navier-Stokes equations. Cambridge texts in applied mathematics. Cambridge: Cambridge University Press; 1995.
  • Majda AJ , Bertozzi AL . Vorticity and incompressible flow. Cambridge: Cambridge University Press; 2001.
  • Dong B , Zhang Z . Global regularity of the 2D micropolar fluid flows with zero angular viscosity. J Differ Equ. 2010;249:200–213.
  • Dong B , Li J , Wu J . Global well-posedness and large-time decay for the 2D micropolar equations. J Differ Equ. 2017;262:3488–3523.
  • Xue L . Well posedness and zero microrotation viscosity limit of the 2D micropolar fluid equations. Math Methods Appl Sci. 2011;34:1760–1777.
  • Chen M . Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscosity. Acta Math Sci Ser B Engl Ed. 2013;33:929–935.
  • Dong B , Wu J , Xu X , et al . Global regularity for the 2D micropolar equations with fractional dissipation, submitted for publication.
  • Wu J . Global regularity for a class of generalized magnetohydrodynamic equations. J Math Fluid Mech. 2011;13:295–305.
  • Shang H , Wu J . Global regularity of 2D fractional magneto-micropolar equation, submitted for publication.
  • Hmidi T , Keraani S , Rousset F . Global well-posedness for Euler-Boussinesq system with critical dissipation. Comm Partial Differ Equ. 2011;36:420–445.
  • Li J , Titi ES . Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Arch Ration Mech Anal. 2016;220:983–1001.
  • Bahouri H , Chemin J-Y , Danchin R . Fourier analysis and nonlinear partial differential equations. Heidelberg: Springer; 2011.
  • Bergh J , Löfström J . Interpolation spaces, An introduction. Berlin: Springer-Verlag; 1976.
  • Miao C , Wu J , Zhang Z . Littlewood-Paley theory and its applications in partial differential equations of fluid dynamics. Beijing: Science Press; 2012. Chinese.
  • Runst T , Sickel W . Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations. Berlin: Walter de Gruyter; 1996.
  • Triebel H . Theory of function spaces II. Basel: Birkhauser Verlag; 1992.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.