Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Solutions of the Equations for Viscoelastic Fluids in Some
  Classes of Large Data   We study the existence and uniqueness of global strong solutions to the
equations of an incompressible viscoelastic fluid in a spatially periodic
domain, and show that a unique strong solution exists globally in time if the
initial deformation and velocity are small for the given physical parameters.
In particular, the initial velocity can be large for the large elasticity
coefficient. The result of this paper mathematically verifies that the
elasticity can prevent the formation of singularities of strong solutions with
large initial velocity, thus playing a similar role to viscosity in preventing
the formation of singularities in viscous flows. Moreover, for given initial
velocity perturbation and zero initial deformation around the rest state, we
find, as the elasticity coefficient or time go to infinity, that (1) any
straight line segment $l^0$ consisted of fluid particles in the rest state,
after being bent by a velocity perturbation, will turn into a straight line
segment that is parallel to $l^0$ and has the same length as $l^0$. (2) the
motion of the viscoelastic fluid can be approximated by a linear pressureless
motion in Lagrangian coordinates, even when the initial velocity is large.
Moreover, the above mentioned phenomena can also be found in the corresponding
compressible fluid case.

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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th