A blow-up criterion for classical solutions to the Prandtl equations.

In this paper, we obtain a blow-up criterion for classical solutions to the two-dimensional Prandtl equations under a monotonicity assumption in weighted Sobolev spaces. Our proof is based on nonlinear energy estimates inspired by Masmoudi and Wong [Commun. Pure Appl. Math. 68, 1683–1741 (2015)] and maximum principles for parabolic equations. [ABSTRACT FROM AUTHOR]