Bulletin of the Korean Mathematical Society (대한수학회보)

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DECAY RESULTS OF WEAK SOLUTIONS TO THE NON-STATIONARY FRACTIONAL NAVIER-STOKES EQUATIONS

  • Zhaoxia Liu (College of Science Minzu University of China)
  • Received : 2023.05.16
  • Accepted : 2023.10.19
  • Published : 2024.05.31
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Abstract

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L2-decay rate of weak solutions, which reveals that L2-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

Keywords

Acknowledgement

This work is supported by NSF of China under Grant No. 12371123.

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