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Volume 27, Issue 3
Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential

Qiu Meng & Hongjun Yuan

DOI: 10.4208/jpde.v27.n3.6

J. Part. Diff. Eq., 27 (2014), pp. 251-267.

Published online: 2014-09

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  • Abstract
We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω⊂ℜ^3. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.
  • Keywords

Strong solutions heat-conductive fluids vacuum Poincaré type inequality non-Newtonian potential

  • AMS Subject Headings

35A05, 35D35, 76A05, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mengqiu15@163.com (Qiu Meng)

hjy@jlu.edu.cn (Hongjun Yuan)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-251, author = {Meng , Qiu and Yuan , Hongjun}, title = {Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {3}, pages = {251--267}, abstract = { We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω⊂ℜ^3. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/5141.html} }
TY - JOUR T1 - Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential AU - Meng , Qiu AU - Yuan , Hongjun JO - Journal of Partial Differential Equations VL - 3 SP - 251 EP - 267 PY - 2014 DA - 2014/09 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n3.6 UR - https://global-sci.org/intro/article_detail/jpde/5141.html KW - Strong solutions KW - heat-conductive fluids KW - vacuum KW - Poincaré type inequality KW - non-Newtonian potential AB - We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω⊂ℜ^3. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.
Qiu Meng & Hongjun Yuan. (2019). Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential. Journal of Partial Differential Equations. 27 (3). 251-267. doi:10.4208/jpde.v27.n3.6
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