Existence results for viscous polytropic fluids with vacuum
Yonggeun Cho,Hyunseok Kim +1 more
253
TL;DR: In this paper, the authors considered the Navier-Stokes equations for viscous polytropic fluids with nonnegative thermal conductivity and proved the existence of unique local strong solutions for all initial data satisfying some compatibility condition.
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About: This article is published in Journal of Differential Equations. The article was published on 15 Sep 2006. and is currently open access. The article focuses on the topics: Polytropic process & Bounded function.
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Citations
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Global Classical Large Solutions to Navier-Stokes Equations for Viscous Compressible and Heat Conducting Fluids with Vacuum
Huanyao Wen,Changjiang Zhu +1 more
TL;DR: A unique global classical solution to the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids is got with large initial data and vacuum.
Global Well-Posedness of the One-Dimensional Compressible Navier--Stokes Equations with Constant Heat Conductivity and Nonnegative Density
TL;DR: This paper considers the initial-boundary value problem to the one-dimensional compressible Navier--Stokes equations for ideal gases and finds that both the viscous and heat conductive coefficients are positive.
Long time existence of the non-isentropic slightly compressible Navier-Stokes equations with boundary conditions
Qiangchang Ju,Jianjun Xu +1 more
TL;DR: Long time existence of smooth solutions for the non-isentropic slightly compressible Navier-Stokes equations with boundary conditions holds under small Mach number.
Blow-up criteria for the navier–stokes equations of compressible fluids
Jishan Fan,Song Jiang +1 more
TL;DR: In this paper, the Navier-Stokes equations of three-dimensional compressible isentropic and two-dimensional heat-conducting flows in a domain Ω with nonnegative density were studied.
Global classical solutions to a 3D Navier–Stokes–Korteweg equations with small initial energy
TL;DR: In this article, the authors investigated the global well-posedness of classical solutions to three-dimensional Cauchy problem of the compressible Navier-Stokes type system with a Korteweg stess tensor under the condition that the initial energy is small.
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