TY - JOUR
T1 - Existence and Uniqueness Results for Viscous, Heat-conducting 3-D Fluid with Vacuum
JO - Journal of Partial Differential Equations
VL - 4
SP - 347
EP - 376
PY - 2008
DA - 2008/11
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5287.html
KW - Compressible Navier-Stokes equations
KW - existence
KW - uniqueness
KW - blow-up
AB -  We prove the local existence and uniqueness of the strong solution to the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. The initial density may vanish in an open set and the domain could be bounded or unbounded. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in R^n (n ≥ 1) when the initial density has compactly support and the initial total momentum is nonzero.