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Global Regularity to the Two Dimensional Compressible Navier-Stokes Equations with Mass Diffusion

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Abstract

For an isentropic compressible Navier-Stokes model with mass diffusion in a two dimensional bounded smooth domain, global existence and uniqueness of strong solution to the initial-boundary value problem is proved, without any size restriction on the initial data. The proof relies on global upper and lower positive bound for the density, which is a consequence of mass diffusion and obtained by De Giorgi-Nash-Moser’s estimate for solution to the second order parabolic equation.

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Acknowledgements

The authors would like to thank the referees for careful reading and pointing out some misprints. The research is supported by NSF of China (Grant Nos. 10931007 and 11171145) and the PAPD of Jiangsu Higher Education Institution.

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  1. Department of Mathematics, Nanjing University, 210093, Nanjing, P. R. China

    Xiaoyun Cai, Zhengzi Cao & Yongzhong Sun

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  1. Xiaoyun Cai
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  2. Zhengzi Cao
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  3. Yongzhong Sun
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Correspondence to Yongzhong Sun.

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Cai, X., Cao, Z. & Sun, Y. Global Regularity to the Two Dimensional Compressible Navier-Stokes Equations with Mass Diffusion. Acta Appl Math 136, 63–77 (2015). https://doi.org/10.1007/s10440-014-9885-0

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