Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong solution for Korteweg system in bmo$^{-1}(\mathbb{R}^N)$ with
  initial density in $L^\infty$   In this paper we investigate the question of the local existence of strong
solution for the Korteweg system in critical spaces in dimension $N\geq 1$
provided that the initial data are small. More precisely the initial momentum
$\rho_0 u_0$ belongs to $\mbox{bmo}_{T}^{-1}(\mathbb{R}^N)$ for $T>0$ and the
initial density $\rho_0$ is in $L^\infty(\mathbb{R}^N)$ and far away from the
vacuum. This result extends the so called Koch-Tataru Theorem for the
incompressible Navier-Stokes equations to the case of the Korteweg system. It
is also interesting to observe that any initial shock on the density is
instantaneously regularized inasmuch as the density becomes Lipschitz for any
$\rho(t,\cdot)$ with $t>0$. We also prove the existence of global strong
solution for small initial data $(\rho_0-1,\rho_0u_0)$ in the homogeneous Besov
spaces $(\dot{B}^{\frac{N}{2}-1}_{2,\infty} (\mathbb{R}^N) \cap
\dot{B}^{\frac{N}{2}}_{2,\infty} (\mathbb{R}^N) \cap L^\infty(\mathbb{R}^N))
\times (\dot{B}^{\frac{N}{2}-1}_{2,\infty} (\mathbb{R}^N))^N$. This result
allows in particular to extend in dimension $N=2$ the notion of Oseen solutions
defined for incompressible Navier-Stokes equations to the case of the Korteweg
system when the vorticity of the momentum $\rho_0 u_0$ is a Dirac mass
$\alpha\delta_0$ with $\alpha$ sufficiently small.

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The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom