A Blow-up Criterion for the Density-Dependent Navier–Stokes–Korteweg Equations in Dimension Two

This paper proves a blow-up criterion for the strong solutions with vacuum to the density-dependent Navier–Stokes–Korteweg equations over a bounded smooth domain in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{2}$\end{document}, which only in terms of the density.