圆型方程多重径向解与Navier-Stokes方程的正则解研究

Study on the Regular Solutions of the Multiple Radial Solutions and Navier-Stokes Equations of Circular Equations

针对圆型方程多重径向解问题,讨论了-△u=λk（︱x︱）f（u）中的椭圆形方程径向解是否存在,证明了f（u）与k（︱x︱）（分别满足一定条件时,得出方程至少存在一个正的径向解,同时证明了边值存在与否对三重径向解的影响。讨论了分数次耗散N-S的方程δ1u＋u·▽u＋▽p=-（-△）^au的正则解。

In view of the problem of multiple radial solutions for circular equations, the existence of the radial solutions of elliptic equations in -△u=λk（︱x︱）f（u） is discussed. It is proved that the equation has at least one positive radial solution when f（u） and k（︱x︱） satisfy certain conditions. At the same time, it is proved that the existence of boundary value or not has an effect on the three radial solution. The regular solution of the δ1u＋u·▽u＋▽p=-（-△）^au equation with fractional dissipation N-S is discussed. By means of some inequalities, it is proved that when 0〈a≤5/4 and 1/2〈a≤5/4 are in the same space, the weak solutions of the equation have regular results in the same space in （0,T] .