标题： 弱解的结构到纳维-斯托克斯方程 显示英文标题

标题： The structure of weak solutions to the Navier-Stokes equations

摘要： 整体空间中纳维-斯托克斯方程的多余解的存在意味着并非所有具有均匀局部有界能量的解都满足有用的局部压力展开。 我们证明，抛物型均匀局部$L^2$类中的每个弱解都可以作为满足分布意义下局部压力展开的解的超伽利略变换得到。 这为一大类解提供了一个强大的表示定理。 我们利用这种结构来获得局部压力展开的充分条件。 显示英文摘要

摘要： The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local pressure expansion. We prove that every weak solution in a parabolic uniformly local $L^2$ class can be obtained as a transgalilean transformation of a solution satisfying the local pressure expansion in a distributional sense. This gives a powerful representation theorem for a large class of solutions. We use this structure to obtain a sufficient condition for the local pressure expansion.