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分数阶不可压缩Navier-Stokes-Coriolis方程周期解的存在性
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Abstract:
本文研究了带有旋转效应的分数阶Navier-Stokes方程在给定周期外力作用下周期mild解的存在唯一性，并且建立了Besov空间中分数阶热半群的线性估计。首先，给出符号及函数空间的定义。其次，采用分数阶热半群的Lp-Lq估计，分别对分数阶不可压缩Navier-Stokes-Coriolis方程的线性项及非线性项进行了估计。最后证明了给定一个具有周期ω的外力f，分数阶不可压缩Navier-Stokes-Coriolis方程周期mild解是唯一存在的，且周期也为ω。
In this paper, we study the existence and uniqueness of periodic mild solution for fractional incompressible Navier-Stokes equations in the rotational framework and establish the linear estimation of fractional heat semigroups in Besov space. Firstly, the definition of symbol and function space is given. Secondly, the linear and nonlinear terms of the fractional incompressible Navier-Stokes-Coriolis equations were estimated by using the Lp-Lq estimates of fractional heat semigroups. Finally, we proved that given an external force with periodic ω, the periodic mild solution of the fractional incompressible Navier-Stokes-Coriolis equation is uniqueness and its period is also ω.
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