Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system   In this paper, we study the vanishing viscosity limit for a coupled
Navier-Stokes/Allen-Cahn system in a bounded domain. We first show the local
existence of smooth solutions of the Euler/Allen-Cahn equations by modified
Galerkin method. Then using the boundary layer function to deal with the
mismatch of the boundary conditions between Navier-Stokes and Euler equations,
and assuming that the energy dissipation for Navier-Stokes equation in the
boundary layer goes to zero as the viscosity tends to zero, we prove that the
solutions of the Navier-Stokes/Allen-Cahn system converge to that of the
Euler/Allen-Cahn system in a proper small time interval. In addition, for
strong solutions of the Navier-Stokes/Allen-Cahn system in 2D, the convergence
rate is c\nu^{1/2}.

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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: hep-th