On the global existence of solutions to the Prandtl's system

AbstractIn this paper we establish a global existence of weak solutions to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik (J. Appl. Math. Mech. 30 (1966) 951) provided that the pressure is favourable. This generalizes the local well-posedness results due to Oleinik (1966; Mathematical Models in Boundary Layer Theory, Chapman & Hall, London, 1999). For the proof, we introduce a viscous splitting method so that the asymptotic behaviour of the solution near the boundary can be estimated more accurately by methods applicable to the degenerate parabolic equations