Volume 21, Issue 4
Existence and Uniqueness Results for Viscous, Heat-conducting 3-D Fluid with Vacuum

Ting Zhang & Daoyuan Fang

J. Part. Diff. Eq., 21 (2008), pp. 347-376.

Published online: 2008-11

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  • Abstract
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.
  • Keywords

Compressible Navier-Stokes equations existence uniqueness blow-up

  • AMS Subject Headings

35Q30 76N10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-21-347, author = {}, title = {Existence and Uniqueness Results for Viscous, Heat-conducting 3-D Fluid with Vacuum}, journal = {Journal of Partial Differential Equations}, year = {2008}, volume = {21}, number = {4}, pages = {347--376}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5287.html} }
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.
Ting Zhang & Daoyuan Fang . (2019). Existence and Uniqueness Results for Viscous, Heat-conducting 3-D Fluid with Vacuum. Journal of Partial Differential Equations. 21 (4). 347-376. doi:
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