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\begin{document}

\title{Global well-posedness for the generalized Navier-Stokes-Coriolis
equations with highly oscillating initial data}



\author[1]{Xiaochun Sun}%
\author[1]{Mixiu Liu}%
\author[2]{Jihong Zhang}%
\affil[1]{Northwest Normal University}%
\affil[2]{Lanzhou City University}%


\vspace{-1em}



  
  \date{June 16, 2024}


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\begin{abstract}
We study the small initial date Cauchy problem for the generalized
incompressible Navier-Stokes-Coriolis equations in critical hybrid-Besov
space
\$\textbackslash{}dot\{\textbackslash{}mathscr\{B\}\}\_\{2,\textbackslash{},
p\}\^{}\{\textbackslash{}frac\{5\}\{2\}-2\textbackslash{}alpha,
\textbackslash{}frac\{3\}\{p\}-2\textbackslash{}alpha+1\}(\textbackslash{}mathbb\{R\}\^{}3)\$
with \$1/2\textless{}\textbackslash{}alpha\textless{}2\$ and
\$2\textbackslash{}leq p\textbackslash{}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\textbackslash{}leq
p\textbackslash{}leq\textbackslash{}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.%
\end{abstract}%



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\textbf{Hosted file}

\verb`Globalwell-posednessforGNSCwithhighlyoscillatinginitialdata.tex`  available at \url{https://authorea.com/users/330488/articles/538669-global-well-posedness-for-the-generalized-navier-stokes-coriolis-equations-with-highly-oscillating-initial-data}

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