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arXiv · 2408.00333

Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity

Xiangdi Huang·Jiaxu Li·Rong Zhang
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Abstract

This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density ($\mu(\rho)=\mu\rho^\alpha$ with $\alpha>1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions.

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Xiangdi Huang, Jiaxu Li, Rong Zhang. 2024-08-01. Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity. https://arxiv.org/abs/2408.00333

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