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Mathematics > Analysis of PDEs

arXiv:1403.1085 (math)
[Submitted on 5 Mar 2014]

Title:Global Small Solutions to a Complex Fluid Model in 3D

Authors:Fanghua Lin, Ting Zhang
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Abstract:In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Beside 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 $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.
Comments: 12 pages
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35Q35, 76W05
Cite as: arXiv:1403.1085 [math.AP]
  (or arXiv:1403.1085v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1403.1085
Related DOI: https://doi.org/10.1007/s00205-014-0822-1

Submission history

From: Ting Zhang [view email]
[v1] Wed, 5 Mar 2014 11:38:13 UTC (12 KB)
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