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arXiv · 1101.5862

Global existence in critical spaces for incompressible viscoelastic fluids

Ting Zhang·Daoyuan Fang
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Abstract

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. We point out a smoothing effect on the velocity and a $L^1-$decay on the difference between the deformation tensor and the identity matrix. Our result implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.

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Ting Zhang, Daoyuan Fang. 2011-01-31. Global existence in critical spaces for incompressible viscoelastic fluids. https://arxiv.org/abs/1101.5862

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