Searching for Singularities in Navier–Stokes Flows Based on the Ladyzhenskaya–Prodi–Serrin Conditions

In this investigation, we perform a systematic computational search for potential singularities in 3D Navier–Stokes flows based on the Ladyzhenskaya–Prodi–Serrin conditions. They assert that if the quantity ∫0T‖u(t)‖Lq(Ω)pdt$$\int _0^T \Vert \textbf {u}(t) \Vert _{L^q(\Omega )}^p \, dt$$, where 2/p+3/q=1$${2/p+3/q = 1}$$, q>3$$q > 3$$, is bounded, then the solution u(t)$$\textbf {u}(t)$$ of the Navier–Stokes system is smooth on the interval …