广义Navier-Stokes方程弱解的正则性

Regularity of Weak Solutions to the Generalized Navier-Stokes Equations

该文研究象征是m(ξ)的广义Navier-Stokes方程弱解正则性.设m(ξ)≥|ξ|~α/g(|ξ|),其中α≥1/2+n/4,g≥1是径向对称非减函数,满足∫_1^(+∞)(ds)/(sg^2(s))=+∞,如果∫_0~t‖u(s)‖_(B_((2,∞)~α))~2 ds<+∞,那么广义Navier-Stokes方程存在唯一整体光滑解.

This paper discusses the regularity of weak solutions to the generalized Navier-Stokes equations with symbol m（ξ）. Assume that m（ξ）≥｜ξ｜a/g（｜ξ｜）,where a≥1/2＋n/4 and g≥1, is radially symmetric, nondecreasing and satisfies f＋∞1ds/sg2（s）=＋∞,If ∫t0｜｜u（s）｜｜2Ba2,∞ds〈＋∞ then the generalized Navier-Stokes equation has a unique global smooth solution.