时空分数阶Navier-Stokes方程解的存在性  

Existence of solutions to time-space fractional Navier-Stokes equation

作　　者：姜自文 王丽真 王路生 JIANG Ziwen;WANG Lizhen;WANG Lusheng(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2024年第3期485-498,共14页Pure and Applied Mathematics

基　　金：国家自然科学基金(12271433).

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BC((0,∞);L_(σ)^(d/α-1,∞)(R^(d)))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.This paper investigate the Cauchy problem of time-space fractional incompressible Navier-Stokes equation and establish the existence and uniqueness of mild solution in Marcinkiewicz spaces.Specifically,utilizing the weak L^(r)-weak L^(q) estimates 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,∞);L_(σ)^(d/α-1,∞)(R^(d))) under some small initial data conditions is obtained.

关 键 词：时空分数阶Navier-Stokes方程 Marcinkiewicz空间 MILD解 存在唯一性 

分 类 号：O175.2[理学—数学]