Regularity Criterion for the Three-dimensional Boussinesq Equations

Abstract

We prove that a solution to the three-dimensional Boussinesq equations does not blow-up at time T if $\Vert u_{\le Q}{\Vert }_{B_{\infty ,\infty }^1}$ is integrable on $(0,T)$, where $u_{\le Q}$ represents the low modes of Littlewood-Paley projection of the velocity $u$.

10 pages, corrected misprints, added a new reference

References in corpus (3)

• Determining modes for the 3D Navier-Stokes equations
• Determining modes for the surface Quasi-Geostrophic equation
• Regularity criteria for the 3D Navier-Stokes and MHD equations