A remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions

作者：Kozono Hideo^*; Terasawa Yutaka; Wakasugi Yuta

来源：Journal of Functional Analysis, 2017, 272(2): 804-818.

DOI：10.1016/j.jfa.2016.06.019

• Navier-Stokes equations
• Finite Dirichlet integral
• Scaling invariance
• Liouville-type theorem

Consider the 3D homogeneous stationary Navier-Stokes equations in the whole space R-3 We deal with solutions vanishing at infinity in the class of the fmite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance.

• 出版日期2017-1-15