Global well-posedness for the generalized Navier-Stokes-Coriolis equations with highly oscillating initial data
• Xiaochun Sun,
• Mixiu Liu,
• Jihong Zhang
Xiaochun Sun
Northwest Normal University

Corresponding Author:sunxc@mail.bnu.edu.cn

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Mixiu Liu
Northwest Normal University
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Jihong Zhang
Lanzhou City University
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## Abstract

We study the small initial date Cauchy problem for the generalized incompressible Navier-Stokes-Coriolis equations in critical hybrid-Besov space $\dot{\mathscr{B}}_{2,\, p}^{\frac{5}{2}-2\alpha, \frac{3}{p}-2\alpha+1}(\mathbb{R}^3)$ with $1/2<\alpha<2$ and $2\leq p\leq 4$. We prove that hybrid-Besov spaces norm of a class of highly osillating initial velocity can be arbitrarily small. and we prove the estimation of highly frequency $L^p$ smoothing effect for generalized Stokes-Coriolis semigroup with $1\leq p\leq\infty$, At the same time, we prove space-time norm estimation of hybrid-Besov spaces for Stokes-Coriolis semigroup. From this result we deduce bilinear estimation in our work space. Our method relies upon Bony’s high and low frequency decomposition technology and Banach fixed point theorem.
19 Aug 2021Submitted to Mathematical Methods in the Applied Sciences
23 Aug 2021Assigned to Editor
23 Aug 2021Submission Checks Completed
10 Sep 2021Reviewer(s) Assigned
16 Jun 2022Review(s) Completed, Editorial Evaluation Pending
16 Jun 2022Editorial Decision: Accept