Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898648 | Journal of Differential Equations | 2018 | 21 Pages |
Abstract
Introducing a new notion of generalized suitable weak solutions, we first prove validity of the energy inequality for such a class of weak solutions to the Navier-Stokes equations in the whole space Rn. Although we need certain growth condition on the pressure, we may treat the class even with infinite energy quantity except for the initial velocity. We next handle the equation for vorticity in 2D unbounded domains. Under a certain condition on the asymptotic behavior at infinity, we prove that the vorticity and its gradient of solutions are both globally square integrable. As their applications, Loiuville-type theorems are obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi,