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Global Large Solutions and Incompressible Limit for the Compressible Navier–Stokes Equations

  • Zhi-Min Chen
  • Xiaoping ZhaiEmail author
Article
  • 34 Downloads

Abstract

The present paper is dedicated to the global large solutions and incompressible limit for the compressible Navier–Stokes system in \(\mathbb {R}^d\) with \(d\ge 2\). Motivated by the \(L^2\) work of Danchin and Mucha (Adv Math 320:904–925, 2017) in critical Besov spaces, we extend the solution space into an \(L^p\) framework. The result implies the existence of global large solutions initially from large highly oscillating velocity fields.

Keywords

Compressible Navier–Stokes equations Incompressible limit Besov spaces Global well-posedness 

Mathematics Subject Classification

35Q35 76N10 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China under the Grants 11601533 and 11571240.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShenzhen UniversityShenzhenChina

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