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- W2074078929 abstract "In this paper, we consider the two-dimensional density-dependent Navier--Stokes equations over bounded domains. First, we derive a new blow-up criterion for strong solutions with vacuum, which involves only the $L^p$-norm of $nabla mu(rho)$. As a corollary, the global existence of strong solutions with vacuum is derived for the constant viscosity. The key idea is the utilization of a lemma proved by Desjardins [Arch. Rational Mech. Anal., 137 (1997), pp. 135--158]. Second, in addition to the blow-up criterion, strong solutions are proved to exist globally when the $L^p$-norm of $nabla mu(rho_0)$ is suitably small, even in the presence of vacuum. This improves all of the previous global existence result where the density needs to be strictly positive." @default.
- W2074078929 created "2016-06-24" @default.
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- W2074078929 date "2014-01-01" @default.
- W2074078929 modified "2023-09-23" @default.
- W2074078929 title "Global Strong Solution with Vacuum to the Two Dimensional Density-dependent Navier--Stokes System" @default.
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- W2074078929 doi "https://doi.org/10.1137/120894865" @default.
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