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arXiv · 1806.04464

Global existence and exponential decay of strong solutions for the inhomogeneous incompressible Navier-Stokes equations with vacuum

Dehua Wang·Zhuan Ye
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Abstract

The inhomogeneous incompressible Navier-Stokes equations with fractional Laplacian dissipations in the multi-dimensional whole space are considered. The existence and uniqueness of global strong solution with vacuum are established for large initial data. The exponential decay-in-time of the strong solution is also obtained, which is different from the homogeneous case. The initial density may have vacuum and even compact support.

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Dehua Wang, Zhuan Ye. 2018-06-12. Global existence and exponential decay of strong solutions for the inhomogeneous incompressible Navier-Stokes equations with vacuum. https://arxiv.org/abs/1806.04464

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