FRACTIONAL NAVIER-STOKES EQUATIONS

被引：21

作者：

Cholewa, Jan W. ^{[1
]}

Dlotko, Tomasz ^{[1
]}

机构：

[1] Univ Silesia Katowice, Inst Math, PL-40007 Katowice, Poland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 08期

关键词：

Navier-Stokes equations; abstract parabolic equations; initial-boundary value problems for pseudodifferential operators; WEAK SOLUTIONS; UNIQUENESS; OPERATOR; POWERS; LR;

D O I：

10.3934/dcdsb.2017149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider fractional Navier-Stokes equations in a smooth bounded domain Omega subset of R-N, N >= 2. Following the geometric theory of abstract parabolic problems we give the detailed analysis concerning existence, uniqueness, regularization and continuation properties of the solution. For the original Navier-Stokes problem we construct next global solution of the Leray-Hopf type satisfying also Duhamel's integral formula. Focusing finally on the 3-D model with zero external force we estimate a time after which the latter solution regularizes to strong solution. We also estimate a time such that if a local strong solution exists until that time, then it exists for ever.

引用

页码：2967 / 2988

页数：22

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