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- Title
Global Existence of Heat-Conductive Incompressible Viscous Fluids.
- Authors
Ye, Xia
- Abstract
In this paper, we consider the Cauchy problem of non-stationary motion of heat-conducting incompressible viscous fluids in $\mathbb{R}^{2}$ , where the viscosity and heat-conductivity coefficient vary with the temperature. It is shown that the Cauchy problem has a unique global-in-time strong solution $(u, \theta)(x,t)$ on $\mathbb{R}^{2}\times(0,\infty)$ , provided the initial norm $\|\nabla u_{0}\|_{L^{2}}$ is suitably small, or the lower-bound of the coefficient of heat conductivity (i.e. $\underline{\kappa}$ ) is large enough, or the derivative of viscosity (i.e. $|\mu'(\theta)|$ ) is small enough.
- Subjects
HEAT conduction; INCOMPRESSIBLE flow; CAUCHY problem; VISCOSITY solutions; COEFFICIENTS (Statistics)
- Publication
Acta Applicandae Mathematicae, 2017, Vol 148, Issue 1, p61
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-016-0078-x