分数阶不可压缩Navier-Stokes-Coriolis方程解的整体适定性  

Global Well-Posedness for the Fractional Navier-Stokes Equations with the Coriolis Force

作　　者：孙小春 吴育联 徐郜婷 Sun Xiaochun;Wu Yulian;Xu Gaoting(Northwest Normal University,College of Mathematics and Statistics,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学物理学报（A辑）》2024年第3期737-745,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601434)。

摘　　要：该文致力于研究带Coriolis力的分数阶Navier-Stokes方程的Cauchy问题.结合半群S的L^(p)−L^(q)及H˙^(5/2−2α)−L^(q)光滑估计,得到了带Coriolis力的分数阶Navier-Stokes方程解的整体适定性以及u0在齐次Sobolev空间H˙_(σ)^(5/2−2α)(R^(3))足够小时的分数阶Navier-Stokes方程具有唯一的整体mild解.We consider the Cauchy problem of fractional Navier-Stokes equations with the Coriolis force.Combining the L^(p)−L^(q) and H˙^(5/2−2α)−L^(q) smooth estimates of semiggroup S,it is proved that the well-posedness of the fractional Navier-Stokes equations with the Coriolis force and these equations possess a unique global mild solution for arbitrary speed of rotation provided the initial data u0 is small enough in H˙_(σ)^(5/2−2α)(R^(3)).

关 键 词：整体适定性 分数阶 NAVIER-STOKES 方程 齐次 SOBOLEV 空间 CORIOLIS 力 

分 类 号：O174.2[理学—数学]