临界Fourier-Besov-Morrey空间中具有科里奥利力的分数阶Navier-Stokes方程的一致适定性和稳定性

A. E. Baraka, Mohamed Toumlilin
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引用次数: 4

摘要

摘要:本文研究了临界Fourier Besov-Morrey空间中具有科里奥利力的分数阶Navier-Stokes方程的Cauchy问题。利用傅立叶局部化理论和Littlewood-Paley理论,我们得到了一个属于临界傅立叶-Besov-Morrey空间的具有小初始数据的局部适定性结果和全局适定性结果。此外我们证明了相应的全局解随着时间的无穷大而衰减为零,并给出了全局解的稳定性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Uniform well-posedness and stability for fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces
Abstract: In this paper, we study the Cauchy problem of the fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces. By using the Fourier localization argument and the Littlewood-Paley theory, we get a local well-posedness results and global well-posedness results with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover; we prove that the corresponding global solution decays to zero as time goes to infinity, and we give the stability result for global solutions.
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