三维不可压缩广义Navier-Stokes方程组在Fourier-Triebel-Lizorkin空间中的适定性  

Well-posedness of 3D incompressible generalized Navier-Stokes system in Fourier-Triebel-Lizorkin spaces

作　　者：敏德载 吴刚 姚卓雅 MIN Dezai;WU Gang;YAO Zhuoya(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2023年第2期145-154,共10页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11771423)资助。

摘　　要：针对三维不可压缩广义Navier-Stokes方程组的柯西问题,研究其在临界Fourier-Triebel-Lizorkin空间^F•^(4-α-3/p)_(p,q)(ℝ^(3))中的适定性问题。利用Fourier局部化方法和Banach不动点定理,证明当p>3/5-α,q≥1或者p=3/5-α,q∈[3/5-α,6/5-α]时,该方程组对适当小的初始值是整体适定的,对大初始值是局部适定的。In this paper,we consider the Cauchy problem for the 3D incompressible generalized Navier-Stokes system and study the well-posedness in critical Fourier-Triebel-Lizorkin spaces ^F•^(4-α-3/p)_(p,q)(ℝ^(3)).Making use of Fourier localization method and Banach fixed point theorem,we proved that if p>3/5-α,q≥1,the system is locally well-posed for large initial data as well as global well-posed for small initial data.Also we established same result for p=3/5-α,q∈[3/5-α,6/5-α].

关 键 词：NAVIER-STOKES方程组 Fourier-Triebel-Lizorkin空间 整体适定性 局部适定性 

分 类 号：O175.2[理学—数学]