具有部分分数阶扩散项的三维Navier-Stokes方程的适定性  

Well-posedness of three dimensional Navier-Stokes equations with partial fractional diffusion terms

作　　者：黄耀芳 李莉 董玉 张洪林 HUANG Yaofang;LI Li;DONG Yu;ZHANG Honglin(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2023年第1期94-102,共9页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(12271276)。

摘　　要：众所周知,具有超耗散(-Δ)^(5/4)的Navier-Stokes方程是适定的.许多学者研究了具有弱超耗散的问题.去除Navier-Stokes方程中一些不同方向的超耗散分量,在一些额外的条件下,可以证明解的存在性和唯一性.本文推导出从u_(2)和u_(3)的方程中去除沿x_(3)方向的超耗散问题解的存在性和唯一性.需要指出的是,如果从所有方程中去除沿x_(3)方向的超耗散,则本方法无法获得此问题的适定性结果.It is a well-known fact that the Navier-Stokes equation with hyperdissipation(-Δ)^(5/4) is well-posed.There are many scholars committing themselves to solving the problem with weaker hyperdissipation.When some components of hyperdissipation in different spatial directions are removed from the Navier-Stokes equations,the existence as well as uniqueness under some extra conditions is thus proved.In this paper,we derive the existence and uniqueness of the problem with hyperdissipation in x_(3) direction removed from the equations of u_(2) and u_(3).It is worth mentioning that the well-posedness result shall not be obtained by the present method if the hyperdissipation in x_(3) direction is removed from all three equations.

关 键 词：NAVIER-STOKES方程 部分耗散 分数阶耗散 超耗散 适定性 

分 类 号：O175.29[理学—数学] O175.4[理学—基础数学]