Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incompressible flow around a small obstacle and the vanishing viscosity
  limit   In this article we consider viscous flow in the exterior of an obstacle
satisfying the standard no-slip boundary condition at the surface of the
obstacle. We seek conditions under which solutions of the Navier-Stokes system
in the exterior domain converge to solutions of the Euler system in the full
space when both viscosity and the size of the obstacle vanish. We prove that
this convergence is true assuming two hypothesis: first, that the initial
exterior domain velocity converges strongly in $L^2$ to the full-space initial
velocity and second, that the diameter of the obstacle is smaller than a
suitable constant times viscosity, or, in other words, that the obstacle is
sufficiently small. The convergence holds as long as the solution to the limit
problem is known to exist and stays sufficiently smooth. This work complements
the study of incompressible flow around small obstacles, which has been carried
out in [1,2,3]
  [1] D. Iftimie and J. Kelliher, {\it Remarks on the vanishing obstacle limit
for a 3D viscous incompressible fluid.} Preprint available at
http://math.univ-lyon1.fr/~iftimie/ARTICLES/viscoushrink3d.pdf .
  [2] D. Iftimie, M. C. Lopes Filho, and H. J. Nussenzveig Lopes. {\it Two
dimensional incompressible ideal flow around a small obstacle.} Comm. Partial
Differential Equations {\bf 28} (2003), no. 1-2, 349--379.
  [3] D. Iftimie, M. C. Lopes Filho, and H. J. Nussenzveig Lopes. {\it Two
dimensional incompressible viscous flow around a small obstacle.} Math. Ann.
{\bf 336} (2006), no. 2, 449--489.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph