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arXiv · 2010.08080

Global existence of weak solutions to the Navier-Stokes equations with temperature-depending viscosity coefficient

Cheng Yu·Bijun Zuo
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Abstract

In this paper, the initial-boundary value problem to the three-dimensional inhomogeneous, incompressible and heat-conducting Navier-Stokes equations with temperature-depending viscosity coefficient is considered in a bounded domain. The viscosity coefficient is degenerate and may vanish in the region of absolutely zero temperature. Global existence of weak solutions to such a system is established for the large initial data. The proof is based on a three-level approximate scheme, the De Giorgi's method and compactness arguments.

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Cheng Yu, Bijun Zuo. 2020-10-16. Global existence of weak solutions to the Navier-Stokes equations with temperature-depending viscosity coefficient. https://arxiv.org/abs/2010.08080

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