Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moving interface in a viscous incompressible flow   We investigate the sharp interface limit of the diffusive interface system
that couples the Allen--Cahn equation with the instationary Stokes system in a
bounded domain in $\mathbb{R}^2$. This model is used to describe a propagating
front in a viscous incompressible flow with the width of the transition layer
being characterized by a small parameter $\varepsilon>0$. For well-prepared
initial data, we show that the solution converges to a limit system that
couples the curve-shortening flow and the Stokes system.

12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
10
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: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex