Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The incompressible limit in $L^p$ type critical spaces   This paper aims at justifying the low Mach number convergence to the
incompressible Navier-Stokes equations for viscous compressible flows in the
ill-prepared data case. The fluid domain is either the whole space, or the
torus. A number of works have been dedicated to this classical issue, all of
them being, to our knowledge, related to $L^2$ spaces and to energy type
arguments. In the present paper, we investigate the low Mach number convergence
in the $L^p$ type critical regularity framework. More precisely, in the
barotropic case, the divergence-free part of the initial velocity field just
has to be bounded in the critical Besov space $\dot B^{d/p-1}_{p,r}\cap\dot
B^{-1}_{\infty,1}$ for some suitable $(p,r)\in[2,4]\times[1,+\infty].$ We still
require $L^2$ type bounds on the low frequencies of the potential part of the
velocity and on the density, though, an assumption which seems to be
unavoidable in the ill-prepared data framework, because of acoustic waves. In
the last part of the paper, our results are extended to the full Navier-Stokes
system for heat conducting fluids.

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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc