A losing estimate for the ideal MHD equations with application to blow-up criterion
Résumé
In this paper we study the blow-up criterion of smooth solution to the ideal MHD equations in R-n. By means of the Fourier frequency localization and Bony paraproduct decomposition, we show a losing estimate for the ideal MHD equations and apply it to establish an improved blow-up criterion of smooth solutions. As a special case, we recover a previous result of Planchon for the incompressible Euler equations.