Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

Abstract

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B_{\infty ,\infty }^{-1}$ that satisfies the conditions that we considered.

13 pages, updated references for v2

References in corpus (2)

• On the global wellposedness of the 3-D Navier-Stokes equations with large initial data
• Sums of large global solutions to the incompressible Navier-Stokes equations