本文考虑Navier-Stokes 方程稳态解的扰动问题. Landau解是轴对称,(-1)-齐 次显式稳态解,在ℝ3中除原点外都是光滑的. 我们将研究Landau解2-扰动问 题的全局2-弱解关于时间的部分正则性. 为此,我们首先考虑了温和解的局部 存在性和唯一性,并介绍了类似于Navier-Stokes方程的弱强唯一性定理. 因为温 和解唯一并有更高的正则性,所以可被视为一族特殊的强解. 我们使用温和解来 研究2-弱解,并最终得到了部分正则性结果.

In this paper, we consider perturbed Navier-Stokes system around Landau solu tions. These explicit stationary solutions are axisymmetric and homogeneous of degree −1 in ∞(ℝ3\{0}) and have exactly one singularity at the origin. We will study the partial regularity about time of Navier-Stokes equations under 2-perturbations. For our purpose, we consider the local existence and uniqueness of mild solutions by providing complete proofs and a weak-strong uniqueness theorem that is analogous to the one for the Navier-Stokes system. Mild solutions can be considered a special family of strong solutions since the solutions are unique and more regular. We use mild solu tions to study the global-in-time 2-weak solution of perturbed Navier-Stokes system and obtain the partial regularity result.