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Local well-posedness of the vacuum free boundary of 3-D compressible Navier–Stokes equations

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Abstract

In this paper, we consider the 3-D motion of viscous gas with the vacuum free boundary. We use the conormal derivative to establish local well-posedness of this system. One of important advantages in the paper is that we do not need any strong compatibility conditions on the initial data in terms of the acceleration.

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Acknowledgements

G. Gui is partially supported by the National Natural Science Foundation of China under Grants 11571279 and 11931013. C. Wang is partially supported by NSF of China under Grant 11701016. Y. Wang is partially supported by China Postdoctoral Science Foundation 8206200009.

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Authors and Affiliations

  1. Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi’an, 710069, China

    Guilong Gui

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Chao Wang & Yuxi Wang

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  1. Guilong Gui
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  2. Chao Wang
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Correspondence to Guilong Gui.

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Communicated by L. Caffarelli.

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Gui, G., Wang, C. & Wang, Y. Local well-posedness of the vacuum free boundary of 3-D compressible Navier–Stokes equations. Calc. Var. 58, 166 (2019). https://doi.org/10.1007/s00526-019-1608-y

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