Remarks on Oldroyd-B and Related Complex Fluids Models

@article{Constantin2010RemarksOO,
  title={Remarks on Oldroyd-B and Related Complex Fluids Models},
  author={P. Constantin and W. Sun},
  journal={arXiv: Analysis of PDEs},
  year={2010}
}
We prove global existence and uniqueness of solutions of Oldroyd-B systems with relatively small data in $\Rr^d$, in a large functional setting ($C^{\alpha}\cap L^1$). This is a stability result, solutions select an equilibrium and converge exponentially to it. Large spatial derivatives of the initial density and stress are allowed, provided the $L^{\infty}$ norm of the density and stress are small enough. We prove global regularity for large data for a model in which the potential responds to… Expand
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