Global Solutions for Incompressible Viscoelastic Fluids
By Zhen Lei, Chun Liu, Yi Zhou. 2008
295 citations recorded by the source corpus.
We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near- equilibrium initial data. The results hold in both two- and three-dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals, and mixture problems.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/5fd94206715c24ce4abbf702c2650c36d58c4ccb
How researchers see this paper
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In Applied Mathematics
- Xianpeng Hu
- Dehua Wang
- Nader Masmoudi
- Song Jiang
- Frédéric Rousset
- Fucai Li
- Qiangchang Ju
- Peter Constantin
In Computational Mechanics
- Xianpeng Hu
- Dehua Wang
- Nader Masmoudi
- Song Jiang
- Frédéric Rousset
- Vlad Vicol
- Peter Constantin
- Fucai Li
Citations in the corpus
- Global Regularity for Some Oldroyd‐B Type Models (2013, unknown): “Many works have been devoted to the proof of global well-posedness in the case of small data after the work of F.H. Lin et al. ([19], [20], [21]).”
- Global Existence for the Multi-Dimensional Compressible Viscoelastic flows (2010, background): “This step for the incompressible case has been fulfilled successfully in [14].”
- Global small solutions to 2-D incompressible MHD system (2013, unknown): “3), we can not apply the ideas and analysis developed in [23, 24, 9, 21] for the viscoelastic fluid system to solve (1.”
- Global existence of weak solutions to macroscopic models of polymeric flows (2011, background): “Global existence for small data was also proved in [31, 29].”