297 research outputs found
Strong solutions of the thin film equation in spherical geometry
We study existence and long-time behaviour of strong solutions for the thin
film equation using a priori estimates in a weighted Sobolev space. This
equation can be classified as a doubly degenerate fourth-order parabolic and it
models coating flow on the outer surface of a sphere. It is shown that the
strong solution asymptotically decays to the flat profile
Weak solutions to lubrication systems describing the evolution of bilayer thin films
The existence of global nonnegative weak solutions is proved for coupled
one-dimensional lubrication systems that describe the evolution of nanoscopic
bilayer thin polymer films that take account of Navier-slip or no-slip
conditions at both liquid-liquid and liquid-solid interfaces. In addition, in
the presence of attractive van der Waals and repulsive Born intermolecular
interactions existence of positive smooth solutions is shown
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