Thomas Ruf

A very short proof of a new energy identity for strong solutions to the Navier-Stokes system in 3D

We prove that strong solutions to the incompressible, homogeneous Navier-Stokes system on $\mathbb{R}^3$ are global in time for initial data in the Sobolev space $H^1_\sigma(\mathbb{R}^3)$. The central ingredient of the proof is a new energy estimate that rules out finite-time blow-up in $L^r(\mathbb{R}^3)$ for $r = 2...