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Global Strong Solution and Exponential Decay of 3D Nonhomogeneous Asymmetric Fluid Equations with Vacuum

Abstract

We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time-weighted techniques.

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Corresponding author

Correspondence to Xin Zhong.

Additional information

Guochun Wu was partially supported by National Natural Science Foundation of China (11701193, 11671086), Natural Science Foundation of Fujian Province (2018J05005, 2017J01562), Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan (2017ZT012). Xin Zhong was partially supported by National Natural Science Foundation of China (11901474), the Chongqing Talent Plan for Young Topnotch Talents (CQYC202005074), and the Innovation Support Program for Chongqing Overseas Returnees (cx2020082).

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Wu, G., Zhong, X. Global Strong Solution and Exponential Decay of 3D Nonhomogeneous Asymmetric Fluid Equations with Vacuum. Acta Math Sci 41, 1428–1444 (2021). https://doi.org/10.1007/s10473-021-0503-8

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  • DOI: https://doi.org/10.1007/s10473-021-0503-8

Key words

  • nonhomogeneous asymmetric fluid equations
  • global strong solution
  • exponential decay
  • vacuum

2010 MR Subject Classification

  • 35Q35
  • 76D03