Internal Flows of Incompressible Fluids Subject to Stick-Slip Boundary Conditions

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• 作者：Miroslav Bulíček ; Josef Málek
• 关键词：Navier–Stokes–Fourier fluid ; Bingham fluid ; No ; slip ; Navier’s slip ; Threshold slip ; Stick ; slip ; Incompressible fluid ; Implicit constitutive theory ; Implicitly constituted boundary condition ; Unsteady flow ; Weak solution ; Long ; time and large ; data existence ; Integrable pressure
• 刊名：Vietnam Journal of Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：45
• 期：1-2
• 页码：207-220
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2305-2228
• 卷排序：45

文摘

We study mathematical properties of internal three-dimensional flows of incompressible heat-conducting fluids with stick-slip boundary conditions, which state that the fluid adheres to the boundary until a certain criterion activates the slipping regime on the boundary. We look at this type of activated boundary condition as at an implicit constitutive equation on the boundary and establish the long-time and large-data existence of weak solutions for the incompressible three-dimensional Navier–Stokes–Fourier system with the viscosity and the heat conductivity depending on the temperature (internal energy). It is essential for our approach to know that the pressure, i.e., the quantity that is a consequence of the fact that the material is incompressible, is globally integrable. While this requirement is in the case of unsteady flows subject to a no-slip boundary condition open for most incompressible fluids, we show that this difficulty can be successfully overcome if one replaces the no-slip boundary condition by a stick-slip boundary condition. The result relies also on the approach developed in Bulíček et al. (Nonlinear Anal. Real World Appl. 10, 992–1015, 10).