An Osgood type regularity criterion for the 2D Oldroyd‐B model

Abstract

By means of the Littlewood‐Paley decomposition and the div‐curl Theorem by Coifman‐Lions‐Meyer‐Semmes, we prove an Osgood type regularity criterion for the 2D incompressible Oldroyd‐B model, that is, sup2≤N<+∞∫0Tfalse∑|j|≤N‖normalΔ˙jτfalse‖L∞NlogNds, where trueΔ˙j denotes the Fourier localization operator whose spectrum is supported in the shell {|ξ|≈2j}.