【摘要】 本文研究了时空分数阶不可压缩Navier-Stokes方程的Cauchy问题并在Marcinkiewicz空间中建立了该方程mild解的存在唯一性.具体地,利用Mittag-Leffler算子在Marcinkiewicz空间的弱L~r-弱L~q估计以及关于时间的连续性和不动点定理,在■空间得到了小初值条件下该方程的全局mild解的存在唯一性.更多还原

【Abstract】 This paper investigate the Cauchy problem of time-space fractional incompressible NavierStokes equation and establish the existence and uniqueness of mild solution in Marcinkiewicz spaces.Specifically,utilizing the weak L~r-weak L~qestimates and time continuity of Mittag-Leffler operators in Marcinkiewicz spaces and the fixed point theorem,the global existence and uniqueness of mild solution in space BC((0,∞);■ under some small initial data conditions is obtained.更多还原