Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence of the Navier-Stokes-Korteweg equations with a
  non-decreasing pressure in $\mathrm{L}^p$-framework   We consider the isentropic Navier-Stokes-Korteweg equations with a
non-decreasing pressure on the whole space $\mathbb{R}^n$ $(n \ge 2)$, where
the system describes the motion of compressible fluids such as liquid-vapor
mixtures with phase transitions including a variable internal capillarity
effect. We prove the existence of a unique global strong solution to the system
in the $\mathrm{L}^p$-in-time and $\mathrm{L}^q$-in-space framework, especially
in the maximal regularity class, by assuming $(p, q) \in (1, 2) \times (1,
\infty)$ or $(p, q) \in \{2\} \times (1, 2]$. We show that the system is
globally well-posed for small initial data belonging to $\mathrm{H}^{s + 1, q}
(\mathbb{R}^n) \times \mathrm{H}^{s, q} (\mathbb{R}^n)^n$ provided $s > n/q$ if
$q \le n$ and $s \ge 1$ if $q > n$. Our results allow the case when the
derivative of the pressure is zero at a given constant state, that is, the
critical states that the fluid changes a phase from vapor to liquid or from
liquid to vapor. The arguments in this paper do not require any exact
expression or a priori assumption on the pressure.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat