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Existence and uniqueness results for viscous, heat-conducting 3-D fluid with vacuum

Ting Zhang·Daoyuan Fang
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Abstract

We consider the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. We prove the local existence and uniqueness of the strong solution in a domain $Ω\subset\mathbb{R}^3$. The initial density may vanish in an open set and $Ω$ could be a bounded or unbounded domain. We also prove a blow-up criterion for the solution. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in $\mathbb{R}^n$ ($n\geq1$) when the initial density has compactly support and the initial total momentum is nonzero.

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Ting Zhang, Daoyuan Fang. 2007-02-07. Existence and uniqueness results for viscous, heat-conducting 3-D fluid with vacuum. https://arxiv.org/abs/math/0702170

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