*Mathematical Methods in the Applied Sciences*Global well-posedness for the generalized Navier-Stokes-Coriolis
equations with highly oscillating initial data

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.

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