We develop a new approach to study the well-posedness theory of the Prandtl equation in
Sobolev spaces by using a direct energy method under a monotonicity condition on the …

We prove local existence and uniqueness for the two‐dimensional Prandtl system in
weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not …

We consider the Navier‐Stokes equations for viscous incompressible flows in the half‐plane
under the no‐slip boundary condition. By using the vorticity formulation we prove the local …

We prove the instability of the Couette flow if the disturbances is less smooth than the
Gevrey space of class 2. This shows that this is the critical regularity for this problem since it …

We investigate the stability of boundary layer solutions of the 2-dimensional incompressible
Navier–Stokes equations. We consider shear flow solutions of Prandtl type: u ν (t, x, y)=(UE …

R.–Il a longtemps été supposé que l'équation de Prandtl n'est bien posée que sous
l'hypothèse de monotonie d'Oleinik, ou pour des données analytiques. Nous montrons …

We show the local in time well-posedness of the Prandtl equations for data with Gevrey 2
regularity in x and Sobolev regularity in y. The main novelty of our result is that we do not …

This note concerns nonlinear ill‐posedness of the Prandtl equation and an invalidity of
asymptotic boundary layer expansions of incompressible fluid flows near a solid boundary …

We consider the Prandtl boundary layer equations on the half plane, with initial datum that
lies in a weighted H 1 space with respect to the normal variable, and is real-analytic with …

We study the well‐posedness theory for the MHD boundary layer. The boundary layer
equations are governed by the Prandtl‐type equations that are derived from the …