On the compressible viscous barotropic flows subject to large external potential forces in a half space with Navier's boundary conditions
• Changzhen Song,
• Jianwen Zhang
Changzhen Song
Xiamen University
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Jianwen Zhang
Xiamen University
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## Abstract

This paper is concerned with an initial and boundary value problem of the Navier-Stokes equations for compressible viscous barotropic flow subject to large external potential forces in a half space $R^3_+$ with Navier’s boundary conditions. The global well-posedness of strongsolutions with large oscillations and vacuum is established, provided that the initial energy is suitably small and that the unique steady state is strictly away from vacuum. As a by-product,the stability of stationary solution is obtained.

#### Peer review status:UNDER REVIEW

26 May 2020Submitted to Mathematical Methods in the Applied Sciences
29 May 2020Assigned to Editor
29 May 2020Submission Checks Completed
15 Jun 2020Reviewer(s) Assigned
09 Aug 2020Review(s) Completed, Editorial Evaluation Pending